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STRUCTURE OF ATOM

John Dalton coined the term atom. The atom is the fundamental particle of matter and
considered to be indivisible and indestructible.
In fact, the atom as the whole is electrically neutral as
number of protons in it is equal to number of electrons.

How small is an atom?

Atoms are very small – they are about 0.00000001 cm wide.
Think about the thickness of a crisp. The number of atoms
you would need to stack up to make the thickness of a crisp,
is approximately the same number of crisps you would need
to stack up to make the height of Mount Everest!
That’s roughly 7 million crisps!
Electron, proton, neutron are the main fundamental particles of an atom.
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Discovery of electron – study of Cathode rays:

J.J. Thomson observed that, when a high voltage is applied between the electrodes
fitted in discharge tube, at a very low pressure, some invisible radiations are emitted
from the cathode. At this stage wall of the discharge tube near cathode starts glowing.

Gas at low
Pressure Discharge tube

Faint green glow

Cathode rays


To vacuum pump

Discharge tube experiment – production of cathode rays

Glowing is due to the bombardment of glass wall by the cathode rays. It may be noted
that when the gas pressure in the tube is 1 atm, no electric current flows through the
tube. This is because the gases are poor conductor of electricity.

Origin of Cathode rays:

Cathode rays are first produced in cathode due to bombardment of the gas molecules by
the high-speed electrons emitted first from the cathode.

Properties of Cathode rays

i. They travel in straight lines with high speed.
ii. They are made up of material particles.
iii. They carry negative charge, the negatively charged material particles constituting the
cathode rays are called electrons.
iv. They produce heating effect.
v. They cause ionization of the gas through which they pass.
vi. They produce X-rays when they strike against the surface of hard metals like tungsten,
molybdenum etc.
vii. They produce green fluorescence on the glass walls of the discharge tube exp: ZnS.
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viii. They affect the photographic plates.

ix. They possess penetrating effect (i.e., they can easily pass-through thin foils of metals).
x. The nature of the cathode rays does not depend upon the nature of the gas, taken
in the discharge tube and the nature of cathode material.
xi. For each cathode rays, the ratio of charge (e) to mass (m) is constant

Discovery of proton – study of Anode rays:

Goldstein discovered the presence of positive rays.
He performed discharge tube experiment in which he took perforated cathode and a
gas at low pressure was kept inside a discharge tube.
On applying high voltage between electrodes, new rays were coming from the side of
anode and passing through the hole in the cathode gives fluorescence on the opposite
glass wall coated with zinc sulphide.
These rays were called anode rays or canal rays or positive rays.

To vacuum pump
H2 gas at low pressure Perforated Cathode
Anode (+)

- +
High voltage
Anode rays Fluorescent ZnS Screen

Origin of anode or positive rays:

In the discharge tube the atoms of gas lose negatively charged electrons. These atoms,
thus, acquire a positive charge. The positively charged particle produced from hydrogen
gas was called the proton.
H→ H+(proton) + e-
Properties of Anode rays:
i) They travel in straight lines. However, their speed is much less than that of the
cathode rays.
ii) They are made up of material particles.
iii) They are positively charged, hence they called as canal rays or anode rays.’
iv) The nature of anode rays depends on the gas taken in the discharge tube.
v) For different gases taken in discharge tube the charge to mass ratio (e/m) of the
positive particles constituting the positive rays is different.
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Fundamental particles:
1) Electron: Electron is a universal constituent discovered by the J.J. Thomson.
 Charge: It was determined by Mullikan by oil drop experiment as -1.602x10-19coulombs
or 4.803x10-10 e.s.u.
 Mass:9.11x10-28g (nearly equal to 1/1837th of mass of hydrogen atom).
 Specific charge:e/m ratio is called specific charge & is equal to 1.76x108 coulombs/gm.
 Mass of one mole of electrons: It is 0.55 mg.
 Charge on one mole of electron is 96500 coulombs or 1 faraday.
 Density: 2.17x1017 g/cc.

2. Proton: (+1p0 or 1H1)

 It was discovered by Goldstein.
 Charge:It carries positive charge i.e.1.602 x 10-19coulombs or 4.803x10-10 esu.
 Mass:1.672x10-24g or 1.672x10-27kg.It is 1837 times heavier than an electron.
 Specific charge (e/m):9.58x104coulomb/gm.

3. Neutron (0n1)
* It was discovered by Chadwick by bombarding Be atom with high speed -particles.
𝟒𝐁𝐞𝟗 + 𝟐 𝐇𝐞𝟒 → 𝟔𝐂
𝟏𝟐
+𝟎 𝐧𝟏
* Charge: Charge less or neutral particle.
* Mass:1.675x10-24 g or 1.675x10-27 kg.
* Density:1.5x1014 g/cm3 and is heavier than proton by 0.18%.
* Specific charge: It is zero.
* Among all the elementary particles neutron is the heaviest and least stable.
Properties of Electron, Proton and Neutron

Properties Electron Proton Neutron

Discovery J.J.Thomson Goldstein Chadwick
-19 -19
Charge -1.6022x10 C 1.6022x10 C Zero
-31 -27
Mass 9.109x10 kg 1.672x10 kg 1.675x10-27 kg
Spin ½ ½ ½
Charge -1 +1 0
Location Outside the nucleus In the nucleus In the nucleus
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Classical Models of Atom:

1) Thomson’s Atomic Model
According to Thomson, an atom is a sphere of positive charge having a number of
embedded electrons in it and sufficient enough to neutralize the positive charge.
This model is compared with a water melon in which seeds are embedded or pudding in
which raisins are embedded. Therefore, this model, sometime called watermelon model
or raisin or plum pudding model.

Limitation: It is failed explain the results of scattering experiment of Rutherford and the
stability of atom.

2) Rutherford’s Atomic Model:

Rutherford, performed -ray scattering experiment in which he bombarded thin foils of
metals like gold, silver, platinum or copper with a beam of fast-moving radioactive particles
originated from a lead block. The presence of 𝛼 particles at any point around the thin foil
of gold after striking it was detected with the help of a circular zinc sulphide screen. The
point at which a𝛼 particle strikes this screen; a flash of light is given out.
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Observations and Conclusions

 particles
ZnS screen

Beam of 
particles + Nucleus

Gold foil (100 nm thickness)

i. Most of the -particles passed through the gold foil without any deflection from
their original path.
Bcz atom has largely empty space as most of the -particles passed through
the foil undeflected.
ii. A few of the alpha particles are deflected fairly at large angles while some are
deflected through small angles.
Bcz there is heavy positive charge at the center of the atom which causes
repulsions.
The entire mass of the atom is concentrated in the nucleus.
iii. A very few -particles are deflected back along their path.
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According to Rutherford,
1. Atom is spherical & mostly hollow with lot of
empty space in it.
2. It has a small +ly charged part at its center
known as nucleus.
3. The nucleus is surrounded by electrons.
Electrons revolve round the nucleus with very
high speeds in circular paths called orbits.
4. The number of extra nuclear electrons is equal to the number of units of positive
charge in the nucleus. Therefore, the atom is electrically neutral. Electrons and the
nucleus are held together by electrostatic forces of attraction.
5. Rutherford’s model has resemblances with solar system. Hence, it’s also known as
planetary model of the atom.
6. There is an empty space around the nucleus called extra nuclear part. In this part
electrons are present. As the nucleus of the atom is responsible for the mass of the
atom, the extra nuclear part is responsible for its volume.

Drawbacks:
1. According to the electromagnetic theory of Maxwell, when a
charged particle moves under the influence of attractive force it
loses energy continuously in the form of electromagnetic
radiation. Therefore, an electron in an orbit will emit radiation.
As a result of this, the electron should lose energy at every
turn and move closer and closer to the nucleus following a spiral path.
Ultimate result is that it will fall into the nucleus thereby making the atom unstable.
i.e., Rutherford’s model cannot explain the stability of the atom.

2. If the electrons lose energy continuously, the

spectrum is expected to be continuous but the actual
observed spectrum consists of well-defined lines of
definite frequencies. Here the loss of energy by
the electrons is not continuous in an atom.
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Atomic number(Z): Atomic number denotes the number of protons or the number of
electrons in the neutral atom.

Atomic number (Z) = Number of protons in the nucleus of an atom or ion

= Number of electrons in a neutral atom.

Each element has a different atomic number.

A The atomic number of sulfur (S) is 16.
B The atomic number of iron (Fe) is 26.
C The atomic number of silver (Ag) is 47.

Each element has a definite and fixed number of protons.

If the number of protons changes, then the atom becomes a different
element.
Changes in the number of particles in the nucleus (protons or
neutrons) are very rare. They only take place in nuclear processes
such as:
⚫ radioactive decay
⚫ nuclear bombs
⚫ nuclear reactors.

Remember!
In an atom… APE!
A= P= E
Atomic number = number of protons = number of electrons

Mass number (A): The mass number is the total number of protons and neutrons
present in the nucleus of an atom of an element and indicated as A.
Protons and neutrons present in the nucleus of an atom are collectively known as nucleons.
Therefore, the mass number is also known as nucleon number.
Mass number (A) = Number of protons (Z) + Number of neutrons (n)
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The number of neutrons (n) in an atom is equal to the difference between the mass
number and the atomic number.
n = A – Z

Mass Number
A A
Atomic Number Z X OR
Z X

Symbol of Element

A tomic number = Protons= Electrons

M ass number = Atomic number+number ofNeutrons

Isotopes, Isobars and Isotones:

Isotopes: The atoms of the same element which have the same atomic number but
different mass numbers are called isotopes.
Exp- 6 C12 , 6C13 , 6C14 , 8 O16 , 8 O17 , 8 O18 , 17 Cl35 , 17 Cl37

hydrogen deuterium tritium

1 proton 1 proton 1 proton

0 neutrons 1 neutrons 2 neutrons

1 electron 1 electron
1 electron

Isotopes of an element differ in the number of neutrons present in the nucleus. But they
have the same number of protons and electrons.
Bcz of same number of electrons they show same chemical properties. They, have
different number of neutrons, so they will have different masses and hence different
physical properties.
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Isobars: The atoms of different elements which have the same mass number but
different atomic numbers are called isobars.
Exp: 18 Ar 40 , 19 K 40 , 20 Ca40
They have same number of nucleons. But they are differed chemically because the chemical
characteristics depend upon the number of electrons which is determined by the atomic
number.
Isotones: Isotones are the atoms of different elements which have the same number of
neutrons.
Eg: 6 C14 , 7 N15 , 8 O16 (n = 8)

14 Si30 , 15 P31, 16 S32 (n = 16)

Isotones show different physical and chemical properties.

Nature of Light (Electromagnetic Radiation):

Electromagnetic radiation do not need any medium for propagation e.g visible, ultra violet,
infrared, x-rays, -rays, radio waves, radiant energy etc.
Two theories were proposed to explain the nature and the propagation of light
i. Corpuscular theory: This theory was proposed by Newton. According to this theory
light is propagated in the form of invisible small particles. i.e. light has particle
nature.
The particle nature of light explained some of the experimental facts such as
reflection and refraction of light but it failed to explain the phenomenon of
interference and diffraction. Therefore, was discarded and ignored.
ii. Wave theory of light (electromagnetic wave theory): was explained by James Clark

Maxwell in 1864 to explain and understand the nature of electromagnetic

radiation.

Features of this theory are:

a) The light is a form of electromagnetic radiations.
b) The light radiations consist of electric and magnetic fields oscillating
perpendicular to each other.
c) Vertical component of wave, ‘E’ indicates
the change in the strength of the
electric field and the horizontal
component of the wave ‘H’ indicates
the change in the strength of the magnetic field.
d) These radiations do not require any medium for propagation.
e) The radiations possess wave character and travel with the velocity of light
i.e. 3x108 m/sec because of the above characteristics, the radiation is called
electromagnetic radiations or waves.
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Electromagnetic radiation is explained by following characteristics:

1. Wave length:
The distance between two successive crests, troughs or between any two consecutive
identical points in the same phase of a wave is called wave length. It is denoted by the
letter (lambda).
The wave length is measured in terms of meters (m), centimeters (cm), angstrom units
(A0) nanometers (nm), picometers (pm) and also in millimicrons (m).
The S.I. unit of wavelength is meter, m

1A0 = 10–10 m or 10–8 cm

1nm = 10–9 m or 10–7 cm = 10A0

1pm = 10–12m or 10–10 cm =10−2 A0

2.Frequency:
The number of waves that pass-through a given point in one second is known as
frequency of radiation. It is denoted by the ‘v’ (nue).

Crest  Crest

a
a 
Trough Trough

Wave motion of the radiation

SI unit of frequency is per second(s–1) or Hertz (Hz). A cycle is said to be completed when
a wave consisting of a crest and a trough passes through a point.

3.Velocity:
The distance travelled by the wave in one second is called velocity or speed of the wave
(C).

SI unit is meters per second (ms–1).

C of electromagnetic radiation in vaccum is a constant commonly called the speed of light
and is denoted by ‘c’.It is equal to 3 × 108ms–1.
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4.Wave number:
The number of waves that can be present at any time in unit length is called wave
number.
It is denoted by  (nue bar).
It is the reciprocal of wave length.
1
Wave number =  =


It is expressed in per centimeter (cm–1) or per meter (m–1).

The SI unit of wave number is m–1.

Wave length, wave number𝝂̅ , frequency 𝝂 and velocity c are related as
.
follows⇒ 𝑪 = 𝜐𝜆

5.Amplitude:
The height of the crest or the depth of the trough of the wave is called amplitude of
the wave. It is denoted by A.
The amplitude determines the strength or intensity or brightness of radiation.

6.Time period:

It is the time taken by the wave for one complete cycle or vibrations. It is denoted by
T. It is expressed in second per cycle.
1 1
T= ( where  = frequency)
𝑉 

Electromagnetic spectrum:
The arrangement of different types of electromagnetic radiations in the order of
increasing wavelengths or decreasing frequencies is known as electromagnetic spectrum.
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 increases
 10-16 10-12 10-10 10-8 10-7 10-6 10-4 10-2 101 106
 decreases
Rays Cosmic - x- Ultra Visible Near Far Micro Radio Long E decreases
rays rays rays violet IR IR wave waves RW

V I B G Y O R

Violet Indigo Blue Green Yellow Orange Red

3800 Å 4300 4800 5300 5800 6300 6900 7600 (in Å)

Limitations of Electromagnetic Wave Theory :

Electromagnetic wave theory was successful in explaining the properties of light such as
interference, diffraction etc.
But it could not explain the following:
(i) The phenomenon of black body radiation.
(ii) The photoelectric effect.
(iii) The change heat capacity of solids as a function of T.
(iv) The line spectra of atoms with special reference to hydrogen.
These phenomena could be explained only if electromagnetic waves are supposed to have
particle nature.

Black body radiation:

When a radiant energy falls on the surface of a body, a part of it is absorbed, a part of it
is reflected and the remaining energy is transmitted.
An ideal body is expected to absorb completely the radiant energy falling on it is known as
a black body. A black body is not only a perfect absorber but also a perfect emitter
of radiant energy.
A hollow sphere coated inside with a platinum black, which has a small hole in its wall can
act as a near black body.
The radiation emitted by a black body kept at high temperature is called black body
radiation. A black body radiation is the visible glow that the solid object gives off when
heated.
A graph is obtained by plotting the intensity of radiation against wave length gives the
following details.
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1. The nature of radiation depends upon the T of the black body.

2. If the energy emitted is continuous the curve should be as shown by the dotted lines.
3. At a given temperature the intensity of radiation increases with the wave length,
reaches maximum and then decreases.
4. The intensity of radiation is greatest at the medium wave lengths and least at highest
and lowest wave lengths.
5. As the temperature increases the peak of maximum intensity shifts towards the
shorter wave lengths.

Planck’s quantum theory:

In order to explain black body radiation, Max Planck proposed quantum theory of radiation.
Postulates
1. Emission of radiation from a body is due to vibrations of the charged particles in the
body.
2. Energy is emitted or absorbed by a body discontinuously in the form of small packets of
energy called quanta.
3. Energy of each quantum of light is directly proportional to the frequency of the radiation.
E   or E = h 
Where ‘h’ is known as Planck’s constant.
The value of ‘h’, 6.6256 × 10–34 Jsec- or 6.6256 × 10–27ergs sec-
4. In case of light, the quantum of energy is called a photon.
Total amount of energy emitted or absorbed by a body is some whole number multiple of
quantum,
E = nh  , where n is an integer such as 1,2,3 . . . . .
This means that a body can emit or absorb energy equal to hv, 2hv, 3hv . . . . . Or any
other integral multiple of h. This is called quantization of energy.
5. The emitted radiant energy is propagated in the form of waves.
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Photoelectric Effect:
When radiations with certain minimum frequency (ν0 ) strike the surface of a metal, the
electrons are ejected from the surface of the metal. It is called photoelectric
effect,electrons emitted are called photoelectron.

For each metal a certain minimum frequency is needed to eject the electrons called as

threshold frequency (  ) which differs from metal to metal.

o
K.E. of photoelectron
K.E. of photoelectron

K.E. constant

o

Frequency of absorbed photon Intensity of Incident radiation

K.E. as a function of frequency K.E. as a function of intensity

It was explained by Einstein. When light of suitable frequency falls on a metal surface, the
light photon gives its energy to the electron of metal atom and the electron is ejected from
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metal surface by absorbing this energy. The minimum energy of a photon required to
eject an electron from a metal is called work function () of the metal. The remaining
part of the energy (h  - ) of photon is used to increase the kinetic energy of the ejected
electron. If o is the threshold frequency and  , the frequency of incident light then
Work function,  = h o .
 According to Einstein, E = h 

 Kinetic energy of photo electron Ek = E -  = h − ho

ATOMIC SPECTRA
Spectrum is the impression produced on a screen when radiations of a particular
wavelengths are analyzed through a prism or diffraction grating. Spectra are broadly
classified into two.
(i) Emission Spectrum.
(ii) Absorption Spectrum.
1. Emission Spectrum: When the radiation emitted from some source, e.g., from the
sun or by-passing electric discharge through a gas at low pressure or by heating some
substance to high temperature etc. is passed directly through the prism and then
received on the photographic plate, the spectrum obtained is called ‘Emission
spectrum’.
Spectrum of a radiation emitted by a substance in its excited state is an emission
spectrum.
Emission Spectrum is of two types:
a. Continuous Spectrum: When white light from any source such as sun, a bulb or any
hot glowing body is analyzed by passing through a prism, it is observed that it splits
up into seven different colors from violet to red, (like rainbow), as shown in fig.

These colors are so continuous that each of them merges into the next. Hence, the
spectrum is called continuous spectrum.
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It may be noted that on passing through the prism, red colour with the longest wavelength
is dedicated least while violet colour with shortest wavelength is deviated the most.
b. Discontinuous Spectrum: When gases or vapours of a chemical substance are heated
in an electric Arc or in a Bunsen flame, light is emitted. If the ray of this light is
passed through a prism, a line spectrum is produced.
• A discontinuous spectrum consisting of distinct and well-defined lines with dark
areas in between is called line spectrum. It is also called atomic spectrum.
• The emission spectrum consisting of a series of very closely spaced lines is called
band spectrum.

Band spectrum is the characteristic of molecules. Hence it is also known as molecular

spectrum. The band spectrum is due to vibrations and rotations of atoms present in a
molecule.

Differences between line and band spectrum

Line spectrum Band spectrum

1. The line spectrum has sharp, 1. The band spectrum has many closed lines.
distinct well-defined lines.

2. The line spectrum is the 2. The band spectrum is characteristic of

characteristic of atoms and is also molecules and is also called molecular
called atomic spectrum. spectrum.

3. The line spectrum is due to transition 3. The band spectrum is due to vibrations and
of electrons in an atom. rotations of atoms in a molecule

4. The line spectrum is given by inert 4. The band spectrum is given by hot metals
gases, metal vapors and atomized and molecular nonmetals.
nonmetals.

2. Absorption spectra: When white light from any source is first passed through the
solution or vapours of a chemical substance and then analyzed by the spectroscope, it is
observed that some dark lines are obtained. Further, it is observed that the dark lines are
at the same place where coloured lines are obtained in the emission spectra for the same
substance.

Difference between emission spectra and absorption spectra

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EMISSION SPECTRA ABSORPTION SPECTRA

1. Emission spectrum is obtained 1. Absorption spectrum is obtained when the
when the radiation from the white light is first passed through the
source are directly analyses in substance and the transmitted light is
the spectroscope. analyzed in the spectroscope.
2. It consists of bright coloured 2. It consists of dark lines in the otherwise
lines separated by dark spaces. continuous spectrum.
3. Emission spectrum can be 3. Absorption spectrum is always
continuous spectrum (if source discontinuous spectrum of dark lines.
emits white light) or
discontinuous, i.e., line spectrum
if source emits some coloured
radiation.

Emission Spectrum of Hydrogen:

When hydrogen gas at low pressure is taken in the discharge tube and the light emitted on
passing electric discharge is examined with a spectroscope, the spectrum obtained is
called the emission spectrum of hydrogen which contain large number of lines which
are grouped into different 5 different series,
• Lyman series,
• Balmer series
• Paschen series
• Brackett series
• Pfund series.
• Humpry series

The wave numbers of all the lines in all the series can be calculated by the Rydberg
equation.
1 1 1
ν̅ = = RZ2 ( 2 − 2 )
λ n1 n2
Where n1 and n2 are whole numbers, n2> n1.

For one electron species like He+, Li2+ and Be3+, the value of R is 109677 cm–1× Z2, where
Z is the atomic number of the species.
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n=7 Humphrey series

n=6
n1=5, n2=6,7,8----
n=5 Pfund series
n1=4, n2=5,6,7,8---- Infra-red region
n=4
Brakett series
n1=3, n2=4,5,6----
n=3 Near
Paschen series

ELECTRONIC TRANSITIONS
Infra-red region

n1=2, n2=3,4,5,6----
υ
n=2
Balmer series Visible region

n1=1, n2=2,3,4,5----
n=1 Lyman series U.V region

Different series of spectral lines in hydrogen emission spectrum

Name of the series n1 n2 Spectral region
Lyman series 1 2,3,4,5,6,7….. Ultraviolet
Balmer series 2 3,4,5,6,7… Visible
Paschen series 3 4,5,6,7…… Near infrared
Brackett series 4 5,6,7…. Infrared
Pfund series 5 6,7…. Far infrared

The wave number for any single electron species like He+, Li2+ and Be3+ can be calculated
1 1
from the equation ν̅ = Z 2 R H (n2 − n2 )
1 2

Bohr’s and Sommerfeld’s Atomic models

To overcome the objections of Rutherford model and to explain the hydrogen spectrum,
Bohr proposed a quantum mechanical model.

POSTULATES OF BOHR’S THEORY

• The electrons revolve round the nucleus with
definite velocity in certain fixed closed circular
paths called orbits (or) shells (or) stationary
state. These shells are numbered as 1, 2, 3, 4 or
termed as K, L, M, N from the nucleus.
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• Each orbit is associated with a definite amount

of energy. As long as an electron is revolving in
an orbit it neither loses nor gains energy.
Hence these orbits are called stationary
states or stable orbits+
• The centrifugal force of the revolving electron
in a stationary orbit is balanced by the
electrostatic attraction between the electron and the nucleus.
• Electron can revolve only in orbits whose angular momentum are an integral multiple
of the factor h/2 π.
nh
mvr = 2π

Where m = mass of electron,

v = velocity of electron,
r = radius of the orbit and
‘n’ is the integral number like, 1, 2, 3, 4 . . . , is called principal quantum number and h =
Planck’s constant
• The energy of an electron changes only when it moves from one orbit to another.
Outer orbits have higher energies while inner orbits have lower energies.
The energy is absorbed when an electron moves from inner orbit to outer orbit.
The energy is emitted when the electron jumps from outer orbit to inner orbit.
• The energy emitted or absorbed in a transition is equal to the difference between
the energies of the two orbits (E2 – E1). Energy emitted or absorbed is in the
form of quanta.
E=E2 – E1 = hv

Here E1 and E2 are the lower and higher allowed energy states.

• Expressions for radius of orbit:

Consider an electron of mass ‘m’ and charge ‘e–’ revolving round the nucleus of charge ‘Ze’
in a circular orbit of radius ‘r’.
Let ‘v’ be the tangential velocity of the electron. As per coulomb’s law, the electrostatic
force of attraction between the moving electron andthenucleus is –Ze2/r.
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For the atom to be stable an equal centrifugal force must act away from the nucleus. This
centrifugal force is equal to –mv2/r, where ‘m’ is the mass of electron and ‘r’ is the radius
of the orbit.
In a stationary orbit
–Ze2 −mv2 Ze2
= or = mv2
r2 r r
𝑛ℎ
As per Bohr’s quantum condition, mvr = 2𝜋
nh 2 𝑛2 ℎ 2
∴v= 2πmror v = 4𝜋2𝑚2 𝑟 2

Substituting the value of v2, we get

Ze2 mn2 h2 n2 h2
or = 4π2 m2r2 or r =
r 4π2 mZe2

Radius for ‘nth’ orbit, rn =

n2 h2
4π2 mZe2

Substituting the standard values, of h, , m and e, we get radius of nth orbit rn =

0.529×n2
A°
Z

For hydrogen, Z=l and n=1 for first orbit,

The radius of the first orbit of hydrogen is 0.529 A0 or 0.0529 nm or 52.9 pm. This value
is known as Bohr’s radius. As the value of n increases, the radius of the orbit will increase.
n 2 h2
In S.I units, rn = 4π2mKZe2
1
Where,K = 4π∈ (ϵ0 = permitivity of air = 8.854 × 10−12 Farad Metre)
0

• Expression for Energy of electron:

The total energy of electron is the sum of kinetic and potential energies.Kinetic energy due
to motion of electron is 2mv2, where m is the mass of electron and v is its velocity.
1

Ze2 Ze2
K.E = 2mv2 =
1
∵ mv 2 =
2r 2r
−Ze2
P.E of electron = 𝑟

Total energy of electron, En = K.E + P.E

Ze2 Ze2 1 Ze2
En= 2r − = −2
r r

Substituting the value of r, we get energy of electron in nth orbit,

−Ze2 4π2 mZe2 −2π2 mZ2 e4
En = or En=
2n2 h2 n2 h2

Substituting the values of m, e, h and𝜋 in the equation, we get

−13.6 ×𝑍2
En = eV per atom
𝑛2
−313.6×𝑍 2
or En = k cal mol–1
𝑛2
−1312×Z2 –1
or En = kJ mol
n2
−2.18×10−11 𝑍 2
or En = erg per atom
𝑛2
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−2.18×10−18 𝑍 2
orEn = j/atom
𝑛2
2π2 mK2 Z2 e4
In S.I units: En = − n2 h2
–1
WhereK = 4𝜋𝜖 and 𝜀𝑜 beingpermittivity of air and is equal to 8.854 × 10–12 Farad metre
1
0

• Derivation of Rydberg equation:

When a gas is subjected to electric discharge or heated by a flame, the electrons in the
ground state of the atom absorb energy and they are promoted to higher quantum states.
As theyare not stable in these states, they emit energy and return to ground state or any
other lower energy states.If E2 is the energy of the higher energy state, E1 is the energy
of the lower energy state and 𝜈 is the frequency of emitted radiation E2 – E1 = h𝜈

If the numbers of the higher and lower energy states are n2 and n1 respectively, En2 =
−2π2 mZe4 1
. n2
h2 2
−2π2 mZe4 1
En1 = . n2
h2 1
−2π2 mZe4 1 1
En2 − En1 = [n2 − n2 ]
h2 1 2
En2 − En1
But En2 − En1 = hcν̅ and ν̅ = ch
1 −2π2 mZe4 1 1
ν̅ = = [ − ]
λ ch2 n21 n22

This equation is similar to Rydberg equation.

1 1 1
[ν̅ = = R × ( 2 − 2 )]
λ n1 n2
2π2 mZ e4
Rydberg constant R should be equal to R = ch3

Substituting the values, we get RH= 1,09,681cm-1.This value is almost equal to Rydberg’s

constant 1,09,677 cm–1.

The frequencies of the spectral lines in the hydrogen spectrum calculated by using Bohr’s
equation are in excellent agreement with the experimental values. This is a concrete
proof of the validity of Bohr’s theory of hydrogen atom.
• Expression for velocity of electron:
As per Bohr’s quantum conditions,
nh nh
mvr = 2π or v = 2πmr
n2 h2
∵ r = 4π2 m Ze2
nh 4π2 m Ze2
∴ v = 2πm × n2 h2

2πZe2
v= cms−1
n
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Substituting the values of 𝜋, e and h in the above expression

2.18×108 ×𝑍 –1
vn= cm s
𝑛
8
Thus the velocity of electron in the first orbit of hydrogen atom is 2.18 ×10 cm s–1.
As the number of the orbit increases, the velocity of the electron decreases.

Explanation of Hydrogen Spectrum by Bohr’s Theory:

Bohr’s theory successfully explains the origin of lines in hydrogen emission spectrum.
Hydrogen atom has only one electron. It is present in K shell of the atom (n = 1). When
hydrogen gas is subjected to electric discharge, energy is supplied. The molecules absorb
energy and split into atoms. The electrons in different atoms absorb different amounts of
energies. By the absorption of energy, the electrons are excited to different higher
energy levels.
Atoms in the excited state are unstable. Therefore, the electrons jump back into different
lower energy states in one or several steps. In each step the energy is emitted in the form
of radiation and is indicated by a line.
Each line has a definite frequency and thus the emission spectrum of hydrogen has many
spectral lines.
• Lyman series are obtained in UV region, when electron returns to the ground state
from higher energy levels 2, 3, 4, 5 ......... and so on.
• Balmer series are obtained in visible region when electron returns to second energy
level from higher energy levels 3, 4, 5, 6 and so on.
• Paschen series are obtained in near infrared region, when electron returns to third
energy level from higher energy levels 4, 5, 6.... And so on.
• Brackett series are obtained in mid infrared region when electron returns to fourth
energy level from higher energy levels 5, 6, 7 . . . and so on.
• Pfund series are obtained in far infrared region when electron returns to the fifth
energy level from higher energy levels 6, 7…….
The maximum number of lines produced when electrons jumps from nth level to ground level
𝑛(𝑛−1)
is equal to, Or ∑(𝑛2 − 𝑛1 )
2
Where, n2 = higher energy level.
n1 = lower energy level.
n = difference in the two energy levels.

Merits and demerits of Bohr’s Atomic model:

1. Bohr’s model explains the stability of the atom. The electron revolving in a stationary
orbit does not lose energy and hence it remains in the orbit forever.
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2. Bohr’s theory successfully explains the atomic spectrum of hydrogen.

3. This theory not only explains hydrogen spectrum but also explains the spectra of one
2+ 3+
electron species such as He+, Li and Be etc.
4. The experimentally determined frequencies of spectral lines are in close agreement
with those calculated by Bohr’s theory.
5. The value of Rydberg constant for hydrogen calculated from Bohr’s equation tallies
with the value determined experimentally.
Limitations of Bohr’s model:
1. Bohr’s theory fails to explain the spectra of multielectron atoms.
2. It could not explain the fine structure of atomic spectrum.
3. It does not explain the splitting of spectral lines into a group of finer lines under the
influence of magnetic field (Zeeman Effect) and electric field (Stark effect).
4. Bohr’s theory predicts definite orbits for revolving electron. It is against the wave
nature of electron.
5. Bohr’s theory is not in agreement with Heisenberg’s uncertainty principle.

Sommerfeld’s Atomic Model:

It is an extension of Bohr’s model. In this model, the electrons in an atom revolve around
the nuclei in elliptical orbit. The circular path is a special case of ellipse. Association of
elliptical orbits with circular orbits explains the fine line spectrum of atoms.
Radial Velocity
Tar velocity
•
Avg Velocity
• major axis
focus

Minor axis

n=4,k=4
n=4,k=3
n=4,k=2

• n=4, k=1, k  0

Sommerfeld’s orbits in hydrogen atom

The main postulates are:
i) The motion of electron in closed circular orbits is influenced by its own nucleus and is
set up into closed elliptical paths of definite energy levels.
ii) The nucleus is one of the foci for all these orbits.
iii) The angular momentum of electron in closed elliptical paths is also quantized i.e. k (h/2),
where k is another integer except zero.
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n length of major axis

iv) The ratio = length of suggests for the possible number of subshells in a shell.
k min or axis

Possible values of k for n = 4 are 1, 2, 3, 4 respectively. For any given value of n, k cannot
be zero as in that case, the ellipse would degenerate into a straight line passing through
the nucleus. When n = k, path becomes circular.

DUAL NATURE OF MATTER (de-BROGLIE’S WAVE THEORY)

Light exhibits different properties such as diffraction, interference, photoelectric
effect, Compton effect, reflection and refraction. The phenomenon of diffraction and
interference can be explained by the wave nature of the light. But the phenomenon of
photoelectric effect and Compton Effect can be explained by the particle nature of
the light. Thus light has dual nature. De-Broglie proposed that matter like radiation, should
also exhibit dual behavior.
hc
Einstein’s generalization of Planck’s theory is given as, E = hν = λ
2
Einstein’s mass energy relationship is E = mc
Equating above two equations, we get
hc 2 h h
= mc or = mc or λ = mc
λ λ
h
Where ‘c’ is the velocity of light. If the velocity of micro particle is ‘v’ then, λ = mV
This is de Broglie’s equation,
Where ‘λ’ is the de Broglie’s wave length, ‘m’ is the mass of the moving particle and ‘h’ is
Planck’s constant.
h
P = mv or λ = P .
Here 𝜆 signifies wave nature and P signifies particle nature.
This is applicable to microparticles like electron, proton, etc., and not applicable for
macrobodies like cricket ball, bullet etc.
The electron moving with high speed possesses both the particle nature and the wave
nature. The waves associated with material particles are known as matter waves or particle
waves.

The Heisenberg’s uncertainty principle:

“It is impossible to determine simultaneously and accurately the exact position and
momentum or velocity of a sub-atomic particle like electron in an atom”.
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One can determine the position of a particle very accurately, and then the determination
of its velocity becomes less accurate. Similarly, one can determine the velocity of a particle
very accurately, and then the determination of its position becomes less accurate. The
certainty in one factor introduces the uncertainty in another factor.
If the uncertainty in the determination of the position of a small particle is given by Δx
and uncertainty in its momentum is Δp, then
ℎ
(Δx) (Δp) ≥ 𝑛𝜋

Where n = 1,2,3,4.........
For an electron revolving around the nucleus in an atom the value of n is nearly 4.
Thus Heisenberg’s principle can also be stated as the product of uncertainty in position and
momentum of an electron like micro particle moving with high speed cannot be less than
h/4.
Heisenberg’s equation can also be written as,
ℎ
(Δx) (Δv) ≥ 4𝜋𝑚

Where m is the mass of the particle and Δv is uncertainty in velocity.

If the position of the particle is known exactly (Δx = 0), Δv becomes infinity (∞) and vice
versa. Heisenberg's uncertainty principle is not applicable to those objects which cannot
change their position by themselves when a light falls on them. It is applicable for micro
particles like electrons.
Significance of Heisenberg’s uncertainty principle:
Like de Broglie equation, although Heisenberg’s uncertainty principle holds good for all
objects but it is significance only for microscopic particles. The reason for this is quite
obvious. The energy of the photon is insufficient to change the position and velocity of
bigger bodies when it collides with them. For example, the light from a torch falling on a
running rat in a dark room, neither change the speed of the rat nor its direction, i.e.,
position.
This may be further illustrated with the following examples:
For a particle of mass 1 mg, we have
ℎ 6.625×10−34 𝑘𝑔𝑚2 𝑠−1
Δx.Δ𝜐 = = = 10−28 𝑚2 𝑠 −1
4𝜋𝑚 4×3.1416×(10−6 𝑘𝑔)

Thus, the product of Δx and Δ𝜐 is extremely small. For particles of mass greater than 1 mg,
the product will still smaller. Hence, these values are negligible.
For a microscopic particle like an electron, we have
ℎ 6.625×10−34 𝑘𝑔𝑚2 𝑠−1
Δx.Δ𝜐 = 4𝜋𝑚 = 4×3.1416×(9×10−31 𝑘𝑔) ≈ 10−4 𝑚2 𝑠 −1
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Classical mechanics, based on Newton’s laws of motion, was successful in explaining the
motion of macroscopic bodies like falling stones or motion of planets around the sun etc.
But it failed when applied to microscopic particles like electrons, atoms, molecules etc.
Hence, new branch introduced called as ‘Quantum mechanics.

Schrodinger Wave Equation:

Quantum mechanics, as developed by Erwin Schrodinger is based on the wave
motionassociated with the particles. The Schrodinger differential wave equation is given
by
∂2 ψ ∂2 ψ ∂2 ψ 8π2 m
+ + + (E − V)ψ
∂x2 ∂z2 ∂y2 h2

Here x, y, z are Cartesian coordinates of the electron

m = mass of electron

h = Planck’s constant

E = total energy of the electron (KE + PE)

V = potential energy of the electron (PE)

ψ= wave function of the electron.
Significance of ψ: ψ is the wave function. It gives the amplitude of the electron wave.

The intensity of light is proportional to the square of amplitude (ψ2). Just as 𝛙2 indicates
the density of photons in space, 𝛙2 in case of electron wave denotes the probability
of finding an electron in the space or probability of finding the electron is also maximum.

The behavior of an electron in an atom is described mathematically by a wave function or

orbital. They are principal quantum number, azimuthal quantum number, magnetic
quantum number and spin quantum number.
‘Set of numbers used to describe energy, size, shape of orbitals in an atom’ called as
quantum numbers.
1.Principal quantum number(n):
• ‘n’ can be any whole number value such as 1,2,3,4, etc. The energy shells
corresponding to these numbers are K, L, M, N, etc.
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• Principal Quantum no. indicates the main energy level to which the electron belongs.
It also indicates the average distance of an electron from nucleus and also the
speed of the atomic electron.
• As the ‘n’ value increases the distance of electron from the nucleus increases and its
energy also increases.
• The maximum no. of electrons that can be present in an orbit is given by 2𝑛2 . The
maximum no. of electron in K, L, M, and N shells are 2,8,18 and 32 respectively.
0.529×𝑛2
• The radius of the orbit is given by the expression: rn = Ao.
𝑍
• The energy of the electron/orbit is given by the expression.
−13.6×𝑍 2
En= cm/sec
𝑛
2.18×108 ×𝑍
• The velocity of the electron is given by the expression. Vn= cm /sec.
𝑛

2. Azimuthal Quantum Number:

• Azimuthal Quantum number was introduced by Sommerfeld’s to explain the fine
spectrum.
• It is also called as secondary quantum no. or orbital angular momentum quantum
number or subsidiary quantum number.
• It is denoted by l.
• ‘l’ can have the values from 0 to (n-1), a total of ‘n’ values. ‘l’ values 0,1,2,3 indicates
s,p,d,f. s,p,d and f are spectroscope terms which indicates sharp. Principle, diffuse
and fundamental respectively.
• Azimuthal Quantum number indicates the sub-shell to which the electron belongs.
It also determines the shapes of the orbital in which the electron is present.
• Each main energy shell can have ‘n’ number of sub-shells.
n l

1 0 (1s)

2 0 (2s), 1 (2p)

3 0 (3s), 1 (3p), 2(3d)

4 0 (4s), 1(4p), 2(4d), 3(4f)

• The orbital angular momentum (L) of an electron is given by the expression: L=

ℎ
√𝑙(𝑙 + 1) 2𝜋

3. Magnetic Quantum number:

• Magnetic quantum number was introduced by Lande to explain Zeeman Effect.
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• It is denoted by m or ml.
• This quantum number refers to different orientations of electron could in a
particular subshell. These orientations are called the orbitals.
• An electron due to its orbital motion around the nucleus generates an electric .This
electric field in turn produces a magnetic field which can interact with the external
magnetic field. Thus, under the influence of the external magnetic field, the
electrons of a subshell can orient themselves in certain preferred regions of space
around the nucleus called orbitals. The magnetic quantum number determines the
number of preferred orientations of the electron present in a subshell.
Since each orientation corresponds to an orbital, therefore, the magnetic quantum
number determines the number of orbitals present in any subshell.
• ‘m’ can have values from – 𝑙 to +𝑙 including zero, a total (2 𝑙+1) values.
Subshell 𝒍 m values No. of orientations (Orbitals)
s 0 0 1
p 1 -1, 0, +1 3
d 2 -2, -1, 0, +1, +2 5
F 3 -3, -2, -1, 0, +1, +2, +3 7
• When l = 0, m has only one value, m = 0. The sub-level‘s’ has one orbital called s orbital.
• When l =1, m can have 3 values m = –1, 0, +1. The sub-level ‘p’ has three space
orientations or three orbitals. The three orbitals are designated as px, py and pz.
• When l = 2, m can have 5 values m = –2,–1, 0, +1, +2. The sub-level ‘d’ has five space
orientations or five orbitals. The five orbitals are designated as d xy, dyz, dzx,
dx2 −y2 and dz2 .
• When l = 3, m can have 7 values m = –3,–2,–1,0,+1,+2,+3. The sub-level ‘f’ has seven
space orientations or seven orbitals.
The magnetic quantum number gives orientation of orbitals in space. All the orbitals
present in a sublevel have same energy and shape. They are called ‘degenerate
orbitals’, which differ in their spatial orientation.
• Each value of ‘m’ constitutes an orbital in the sublevel.
• Maximum no. of electrons in subshell : 2(2𝑙+1) or (4 𝑙+2).

4. Spin Quantum Number:

• Spin Quantum number was proposed by Uhlenbeck and Goudsmith.
• It is denoted by ‘s’ or ‘ms’.
• It indicates the direction of spinning of electron present in any orbital.
• Since the electron in an orbital can spin either in the clockwise direction or in anti-
clockwise direction, hence for a given value of m, s can have only two values, i.e., +1/2
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and -1/2 or these are very often represented by two arrows pointing in the opposite
direction, i.e.,↑and ↓.

If an orbital contains 2 electrons, the two magnetic moments oppose and cancel each other.
Thus, in an atom, if all the orbitals are fully filled, net magnetic moment is zero and the
substance is diamagnetic (i.e., repelled by the external magnetic field). However, if some
half-filled orbitals are present, the substance has a net magnetic moment and is
paramagnetic (i.e., attracted by the external magnetic field).
• The spin angular momentum (𝜇 s) of an electron is given by
h
μs = √s(s + 1) 2π

Atomic Orbital:
The three-dimensional space around the nucleus where the probability of finding the
electron is maximum is called an atomic orbital.
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Differences between orbit and orbital:

Orbit Orbital
1. n orbit is a well-defined circular 1. An orbital is the region of space around
path 1. An orbital is the region of the around the nucleus where the
space around the probability of finding the electron is
around the nucleus in which the maximum (95%)
electron revolves.
2. An orbit represents the movement of 2. An orbital represents the movement of
electron in one plane. electron in three dimensional spaces.
3. An orbit means the position as well as 3. In an orbital it is not possible to find the
the velocity of the electron can be position as well as velocity of the
known with Certainty. electron can be known with certainty.
4. Orbits are circular or elliptical shaped. 4. They have different shapes like
spherical, dumbbell etc
Orbitals have different shapes. s-
orbital is Spherical and p orbital is
dumb bell shaped.
5. Orbits do not have directional 5. Except ‘s’ orbitals, all other orbitals
characteristics. have directional characteristics
6. An orbit can have a maximum number 6. An orbital can accommodate a
2
of2n electrons. maximum of only two electrons.

Node- The three-dimensional space around the nucleus where the probability of
finding the electron is minimum or zero.

Types of Nodes:
Nodes are of two types: a) Radial Node b) Angular Node
A radial node is the spherical region around then nucleus, where the probability if finding
the electron is zero (Ψ2 = 0).
Similarly,nodal plane(angular plane) have zero probability of finding electron.
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Calculation of no. of nodes:

No. of Radial nodes = n−𝑙 − 1
No. of angular nodes = 𝑙
Total no. of nodes = n-1
Ex: In a 3p -orbital
No. of Radial nodes = 3-1-1 = 1
No. of angular nodes = 1
Total no. of nodes = 2.

Shapes of Orbitals:
• s –Orbitals: s- Orbital can accommodate electrons with l = 0 and these orbitals are
present in every orbit starting from 1st orbit.

Orbital in which e-s with n=1 , l = 0 are present is called 1s - orbital.

All s-orbitals are spherical in shape and the size of sphere increases with ‘n’ value. s -
Orbitals are spherically symmetrical because the probability of finding the electron around
the nucleus is same in all directions.
• p – Orbitals:

p- Sublevel begins from 2nd orbit.

For p - sublevel l = 1, indicates
that each p - sub level contains
three orbitals with ‘m’ values –1, 0,
+1. These are designated as px, py
and pz, depending on the axis in which electron density is present.

In px-orbital, electron density is concentrated along the x-axis.

p-Orbitals have dumb-bell shape. Each p -orbital has two lobes separated by one nodal
plane. The probability density function is zero on the plane where the two lobes touch each
other. The nodal planes for px, py and pz - orbitals are YZ, ZX and XY - planes respectively.

The three orbitals present in a given p - sublevel will have same shape, size and energy but
different orientations (differ in m value). These three orbitals are perpendicular to each
other and the angle between any two p - orbitals is 90o.
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• d - Orbitals:begins from 3rd orbit (n = 3). For d- sub level l= 2, indicates that each
d - sublevel contains five orbitals with ‘m’ values –2, –1, 0, +1, +2. These are designated
as dxy,dyz,dzx, 𝑑𝑥 2−𝑦 2 and d𝑧 2 .

All the d-orbitals (except d𝑧 2 ) have double dumb-bell shape. Each d-orbital has four lobes
separated by two nodal planes.
In case of dxy, dyz and dzxorbitals, lobes are present in between the corresponding axes.
i.e.,between x and yaxis in case of dxy orbital. Whereasin d𝑥 2 −𝑦 2 and d𝑧 2 orbitals lobes are
present along the axes. dxy Orbital contains yz and zx as nodal planes. dyz and dzx contain
(xy,zx) and (xy,yz) planes respectively. d𝑥 2 −𝑦 2 orbitalcontains two nodal planes perpendicular
to each other and which make an angle of 45o with respect to x and y axes. 𝑑𝑧 2 orbital does
not contain nodal planes.
5 dorbitals present in a given d- sublevel will have same energy in the ground state.

ENERGY OF ORBITALS
The energy of an electron in a hydrogen atom is determined only by the principal quantum
number. Within a shell, all hydrogen orbitals have the same energy, independent of the
other quantum numbers.
1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f
Although the shapes of 2s and 2p orbitals are different, an electron has the same energy
when it is in 2s orbital or 2p orbital. The energy of an electron in a multielectron atom
depends, not only on its principal quantum number, but also on its azimuthal quantum number.
The s, p, d and f orbitals within a given shell have slightly different energies in a multi
electron atom.
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Electronic configuration of multi electron atoms:

The distribution and arrangement of electrons in the main shells, subshells and orbitals
of an atom is called electronic configuration of the element.

• Aufbau Principle:
“In the ground state of the atoms, the orbitals are filled in order of their increasing
energies”.
In other words electrons first occupy the lowest energy orbital available to them and enter
into higher energy orbitals only after the lower energy orbitals are filled.
The relative energy of an orbital is given by
(n + l ) rule. As (n + l) value increases, the energy of orbital increases.
• The orbital with the lowest (n + l) value is filled first.
• When two or more orbitals have the same (n +l) value, the one with the lowest
‘n’ value (or) highest ‘l ’ value is preferred in filling.
Exp- Consider two orbitals 3d and 4s.
n+l value of 3d = 3 + 2 = 5 and of 4s = 4 + 0 = 4. Since 4s has lowest(n +l) value, it is filled
first before filling taking place in 3d.
Consider the orbitals 3d, 4p and 5s
The (n + l) value of 3d = 3 + 2 = 5
The (n +l) value of 4p = 4 + 1 = 5
The (n +l) value of 5s = 5 + 0 = 5
These three values are same. Since the ‘n’ value is lower to 3d orbitals, the electrons prefer
to enter in 3d, then 4p and 5s.
The order of increasing energy of atomic orbitals is:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d <
6p < 7s and so on.
The sequence in which the electrons occupy various orbitals can
be easily remembered with the help of Moeller’s diagram as
shown in Fig

• Pauli’s Exclusion principle:stated as “No two electrons

in an atom can have the same set of values for all the
four quantum numbers”. This means that two electrons in
an orbital may have the same n, same l and same m but
differ in spin quantum number. In an orbital if one
electron has clockwise spin, the other has anticlockwise
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spin. It follows that an orbital can hold a maximum of two electrons with opposite
spins.
Exp- helium atom has two electrons in its 1s orbital. Quantum numbers for first electron
are n =1, l = 0, m = 0 and s = +1/2. Quantum numbers for second electron are:
n =1, l = 0, m =0, s = –1/2.
The two electrons have the same value for n, same value for l and same value for m but
differ in s.

• Hund’s rule of maximum multiplicity:

According to this rule, when electrons are filled in degenerate orbitals of a subshell,
pairing of an electron takes place only when each orbital of the subshell is filled with
one electron each.It can be also stated that, in ground state of an atom, the
configuration which has more number of unpaired electrons is most stable.
Thus in s, p, d and f subshells, pairing starts from 2nd, 4th, 6th and 8th electrons respectively.
Ex: Electronic configuration of N (7) is 1s2 2s2 2p3.
The electrons in 2p subshell are occupied sing ally. i.e., 1s2 2s2 2𝑝𝑥1 2𝑝𝑦1 2𝑝𝑧1
Electronic configuration of elements from 1 to 30
1 H 1s1 1s1
2 He 1s2 1s2
3 Li 1s2 2s1 [He] 2s1
4 Be 1s2 2s2 [He] 2s2
5 B 1s2 2s2 2p1 [He] 2s2 2p1
6 C 1s2 2s2 2p2 [He] 2s2 2p2
7 N 1s2 2s2 2p3 [He] 2s2 2p3
8 O 1s2 2s2 2p4 [He] 2s2 2p4
9 F 1s2 2s2 2p5 [He] 2s2 2p5
10 Ne 1s2 2s2 2p6 [He] 2s2 2p6
11 Na 1s2 2s2 2p6 3s1 [Ne] 3s1
12 Mg 1s2 2s2 2p6 3s2 [Ne] 3s2
13 Al 1s2 2s2 2p6 3s2 3p1 [Ne] 3s2 3p1
14 Si 1s2 2s2 2p6 3s2 3p2 [Ne] 3s2 3p2
15 P 1s2 2s2 2p6 3s2 3p3 [Ne] 3s2 3p3
16 S 1s2 2s2 2p6 3s2 3p4 [Ne]3s2 3p4
17 Cl 1s2 2s2 2p6 3s2 3p5 [Ne] 3s2 3p5
18 Ar 1s2 2s2 2p6 3s2 3p6 [Ne] 3s2 3p6
19 K 1s2 2s2 2p6 3s2 3p6 4s1 [Ar] 4s1
20 Ca 1s2 2s2 2p6 3s2 3p6 4s2 [Ar] 4s2
21 Sc 1s2 2s2 2p6 3s2 3p6 3d1 4s2 [Ar] 3d1 4s2
22 Ti 1s2 2s2 2p6 3s2 3p6 3d2 4s2 [Ar] 3d2 4s2
23 V 1s2 2s2 2p6 3s2 3p6 3d3 4s2 [Ar] 3d3 4s2
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24 Cr 1s2 2s2 2p6 3s2 3p6 3d5 4s1 [Ar] 3d5 4s1
25 Mn 1s2 2s2 2p6 3s2 3p6 3d5 4s2 [Ar] 3d5 4s2
26 Fe 1s2 2s2 2p6 3s2 3p6 3d6 4s2 [Ar] 3d6 4s2
27 Co 1s2 2s2 2p6 3s2 3p6 3d7 4s2 [Ar] 3d7 4s2
28 Ni 1s2 2s2 2p6 3s2 3p6 3d8 4s2 [Ar] 3d8 4s2
29 Cu 1s2 2s2 2p6 3s2 3p6 3d10 4s1 [Ar] 3d10 4s1
30 Zn 1s2 2s2 2p6 3s2 3p6 3d10 4s2 [Ar] 3d10 4s2

Stability of atoms
Extra stability is associated with atoms in which degenerate orbitals are either half-filled
or completely filled due to
(1) Symmetrical distribution of electrons
(2) Exchange energy. Greater the exchange energy greater is the stability.
The presence of half-filled and completely filled degenerate orbitals gives greater
stability to atoms.
1
It is for this reason the electronic configurations of Cr and Cu are represented as [Ar] 4s
5 1 10
3d and [Ar] 4s 3d respectively.
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SELF ASSESSMENT

1.1 : Introduction :
Q.1. Who introduced the term 'atom'?
Ans: i. A Greek Philosopher Democritus introduced the term atom.
ii. The word 'atom' was derived from Greek word 'a-tomic' meaning indivisible.
Note: Maharshi Kanad, an Indian Saint and Philosopher, first used the term 'Permanu'
(Sanskrit, meaning atom) to describe the ultimate particle of matter.
Q.2. State the postulates of Dalton's atomic theory.
Ans: Postulates of Dalton's atomic theory:
i. Matter is composed of indivisible atoms.
ii. All the atoms of a given element have identical properties. They have identical mass. Atoms
of different elements have different masses.
iii. Atoms of different elements combine in a fixed ratio of whole numbers to form compounds
of different elements.
iv. Chemical reactions involve reorganization of atoms. They are neither created nor
destroyed during chemical reaction.
Q.3. What are fundamental particles?
Ans: i. Sub-atomic particles which are the constituents of an atom are called fundamental particles.
ii. Electron, proton and neutron are the most important fundamental particles of an atom.
Q.4. Explain the discovery of electrical nature of matter.
Ans: i. It is observed that when the substances like glass or ebonite are rubbed with silk or fur,
electricity is produced indicating their electrical nature.
ii. Michael Faraday showed that electricity could be passed through the solution of certain
substances (electrolytes).
iii. When electric current is passed through the solution of an electrolyte, chemical changes
occur in the solution. He called these changes as electrolysis.
iv. During electrolysis, the charged particles migrate towards oppositely charged electrodes
and either accumulate on them or escape as a gas.
v. Thus, matter is electrical in nature.
Note: Faraday surmised his finding in the form of Faraday's laws of Electrolysis. They give a
quantitative relationship between amount of electricity and mass of substance. They mean that
electricity is discrete in nature. Later on, the discrete particles of electricity were called as
electrons.

1.2 : Discovery of electron :

Q.5. What were the observations of scientists who made an attempt to pass electricity
through gases?
Ans: i. Crookes (1879), Julius Plucker (1889) and J. J. Thomson (1896) made an attempt to pass
electricity through gases.
ii. They observed that electricity can be passed through gases by applying a high voltage at
very low pressure.
Q.6. What is done in discharge tube experiments?
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Ans: In discharge tube experiments the electricity is passed through gases at low pressure.
Q.7. Describe the discharge tube experiment of J.J. Thomson.
OR
How are cathode rays produced in a discharge tube?
Ans: Discharge tube experiment of J.J. Thomson:
J.J. Thomson studied the properties of cathode rays through a simple discharge tube
experiment. It can be described as follows:
Gas at low
Apparatus: Pressure Discharge tube

i. A discharge tube is a perfectly leak

proof hard glass tube. The metal electrodes Faint green glow

are fused in the walls. Cathode rays


ii. The tube is connected to a high
efficiency vacuum pump which can
To vacuum pump
evacuate the tube to any desired
pressure.
iii. The tube is filled with the gas under study.

Procedure:
i. The glass tube is evacuated using a vacuum pump.
ii. It is filled with a gas at a very low pressure (10–2 to 10–3 mm Hg.)
iii. A very high voltage of about 5000 V to 10,000 V is applied between the two electrodes in
the tube, which results in the electric discharge between the two electrodes and the gas
in the tube begins to glow.
iv. A high vaccum is created within the tube, the glow is replaced by faint luminous rays from
the cathode. These rays produce fluorescence on the glass opposite to the cathode.
v. The rays start from the cathode and move away from it at right angles in straight lines.
These rays are known as cathode rays.

Q.8. What are cathode rays?

Ans: The rays produced from the cathode of a discharge tube and which move away from it at right
angles towards anode In straight lines are called cathode rays. The cathode rays consist of
negatively charged particles called electrons.
Q.9. Enlist the various properties of cathode rays.
OR
What are the different properties of cathode rays?
Ans: Properties of cathode rays:
i. Cathode rays travel in straight lines away from the cathode. eo' cast shadows of metallic
objects placed in their path.
ii. They cause mechanical motion of a small pin-wheel placed in energy. Hence, they are
material particles.
iii. When cathode rays strike the glass wall of the discharge tube, they produce
phosphorescence
iv. When metal foil is striked with cathode rays, it becomes red and starts glowing
v. On striking with a metallic target, they produce X-rays.
vi. They are deflected by both electric and magnetic fields. This shows they are negatively
charged minute particles.
vii. They ionize gases through which they pass.
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Q.10. Explain the experiment carried out by Sir J.J. Thomson to determine the charge to m
cathode ray particles.
Ans: i. Sir J.J. Thomson determined the ratio of electrical charge (e) to the mass (m) of Cathode
ray particle. He used a specially designed cathode ray tube. The method is described below.
ii. Electrical and magnetic fields are applied. Initially, the cathode rays were allowed to travel
through the tube in the absence of electric and magnetic field. It was observed that
cathode rays originated at cathode, passed through the hole in anode and striked the ZnS
fluorescent screen at point Y.
iii. When electric field of fixed strength was applied, deflection of cathode rays towards
positive electrode was observed and they striked the screen at point X.
iv. When instead of electric field, magnetic field was applied at right angles to the electric
field, deflection of cathode rays in opposite direction was observed and they striked the
screen at point Z as shown in the adjacent diagram.
v. Thomson then subjected the cathode rays to electric field of appropriate voltage such
that they striked at point X on the screen. Now along with the electric field, he subjected
the cathode rays to the magnetic field of field strength H such that the effect due to
electric field is compensated by magnetic field and cathode rays were once again brought
back to the original point Y. The electric and magnetic fields were applied perpendicular
to each other as well as to the path of rays.
vi. Thomson carried out the experiment at different strengths of electric and magnetic fields
and different energies of cathode rays. He observed that the extent of deviation of the
particles from their path in the presence of electric or magnetic field was dependent on
the voltage applied across the electrodes and opposing magnetic field strength
respectively. He accurately measured the magnitude of deflection and determined the
charge to mass ratio (elm) of cathode ray particles as,
𝒆
= 𝟏. 𝟕𝟓𝟖𝟖𝟐𝟎 × 𝟏𝟎𝟏𝟏 𝑪𝒌𝒈−𝟏
𝒎
where m = mass of particle of cathode rays in kg.
e = charge on particle of cathode rays in coulomb (C).
Note:
Cathode ray particles are negatively charged and therefore, this charge is represented as –e.
Q.11. What were the conclusions of cathode ray tube experiments made by Sir J.J. Thomson?
Explain the importance of these conclusions.
Ans: i. After conducting several experiments using specially designed cathode ray tube, Sir J.J.
Thomson concluded that irrespective of the nature of gas used in the discharge tube and
the nature of material of which the cathode was made; the value of elm for a cathode ray
particle was the same.
ii. These conclusions proved that
a. all the constituent particles of cathode rays are identical.
b. the cathode ray particles are the universal constituents of all the atoms of all matter.
Note: A Dutch physicist H.A. Lorenz named the cathode ray particles as electrons.
Q.12. Explain how the mass of electron was determined?
Ans: i. From oil drop experiment, Millikan determined the value of charge present on an electron.
ii. He found that the charge on the electron (e) is equal to – 1.6 × 10–19C. The accepted value
of electrical charge is – 1.6022 × 10-19C.
𝒆
iii. The value of the ratio of charge to mass of electrons = = 𝟏. 𝟕𝟓𝟖𝟖𝟐𝟎 × 𝟏𝟎𝟏𝟏 𝑪𝒌𝒈−𝟏
𝒎
iv. By knowing the charge on the electron (by Millikan method) and elm value (by Sir J.J.
Thomson's experiment) it was possible to determine the mass of electron(m) as follows:
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–
𝒆 𝟏.𝟔𝟎𝟐 × 𝟏𝟎 𝟏𝟗 𝐂
m= = = 9.1094 × 10–31 kg
𝒆/𝒎 𝟏.𝟕𝟓𝟖𝟖𝟐𝟎×𝟏𝟎𝟏𝟏 𝑪𝒌𝒈−𝟏
Note: Mass of electron is the mass of hydrogen atom.
Q.13. Define electron.
Ans: An electron is a subatomic particle which bears unit negative charge i.e. 1.6022 × 10–19 C and
has a mass of 9.1094 × 10–31 kg
1.3 : Discovery of proton :
Q.14. What are canal rays or anode rays or positive rays?
Ans: The rays consisting of positively charged particles produced in a discharge tube by the removal
of electrons from the gaseous atoms and which move away from anode towards cathode in
straight lines are called canal rays or anode rays or positive rays. The canal rays produced from
gaseous hydrogen atoms are protons.
Q.15. How were canal rays or anode rays or positive rays discovered?
Ans: i. E. Goldstein used a modified cathode ray tube for the electrical discharge experiment.
ii. In this method, a perforated disc cathode was used in place of disc cathode. When the gas
pressure was not too low, in addition to
Perforated cathode
cathode rays, a new kind of rays were also
H gas at low pressure
found streaming behind the cathode.
2
Anode rays

iii. These rays travelled in opposite direction

to the cathode rays.  ZnS coating

iv. These rays travel through the holes of

the cathode in the form of a stream or
canal. They produced a glow on the other H.V.
To vacuum pump

end of the discharge tube i.e. cathode.

v. Goldstein called them Canal rays or Anode rays.
vi. These rays consist of +ve charged particles. These are also known as Positive rays.

Q.16. State the properties of canal ray?

Ans: Properties of canal rays:
i. Canal rays travel in a straight line. The direction of travel is opposite to the cathode rays.
ii. Canal rays get deflected towards the negative electrode in the presence of el indicating
that the constituent particles of canal rays are positively charged.
iii. Fluorescence is produced when canal rays are made to fall on the zinc sulphide.
iv. They are also affected by a magnetic field which confirms the presence of +ve particles.
v. The charge to mass ratio of the particles is dependent on the gas in the discharge tube.
vi. The positively charged particles carry a positive electrical charge which is a whole number
multiple of the fundamental unit of charge.
vii. Behaviour of the particles in magnetic & electric fields is opposite to that observed for
electrons.
Q.17. How was proton discovered?
Ans: i. After the discovery of canal rays, several attempts were made in order to find the lightest
particle carrying the unit positive charge.
ii. On analyzing the canal rays produced by using various gases, it was found that the lightest
particle having a unit positive charge could be obtained in the discharge tube by using
hydrogen gas.
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iii. These particles of hydrogen gas were found to possess minimum mass and a unit positive
charge. Hence, their value of elm was found to be maximum.
iv. On determining the mass of these particles, it was found that the mass of each particle
was 1837 times the mass of an electron. This particle was called proton.
Note:
i. E. Goldstein (1896) discovered protons in the discharge tube containing hydrogen gas.
𝐻2 → 2𝐻 + + 2 𝑒 −
Protons
ii. The presence of proton was further confirmed by radioactive disintegration.
Q.18. How are positive rays or canal rays produced in the discharge tube?
Ans: i. When high speed electrons (cathode rays) strike neutral atoms or molecules of the gas
contained in the discharge tube, formation of positively charged ions takes place by
removal of one or more electrons from the neutral atoms or molecules of the gas.
𝑀 + 𝑒− → 𝑀+ + 2 𝑒 −
−
𝑀 + 𝑛𝑒 → 𝑀𝑛+ + (𝑛 + 𝑙) 𝑒 −
ii. These positively charged ions move towards perforated cathode and constitute the beam
of positive rays or canal rays coming through the holes of the cathode.
iii. Positive ions that constitute the positive rays can also be produced by passing the electric
discharge through a gas under high electric potential.
Note: Depending upon the number of electrons lost by the atoms or molecules of a gas, the
positively charged ions thus formed carry corresponding amounts of positive charge.
Q.19. Describe the nature of protons as studied by Sir J.J. Thomson.
Ans: Sir J.J. Thomson studied the nature of positive rays. He proposed the following facts about
protons:
i. The actual mass of a proton is 1.672 × 10–24 gram. On the relative scale, a proton has the
mass of approximately 1.00727 atomic mass unit (amu).
ii. Electrical charge of a proton is equal in magnitude & opposite in sign to that of the electron.
A proton carries a charge of + 1.60 × 10–19 Coulombs or +1 elementary charge unit.
iii. Proton was the lightest positive particle found in atomic beams in the discharge tube. It
was considered a unit present in all other atoms.
Q.20. How was it confirmed that all atoms contain proton?
Ans: i. Proton was the lightest positive particle found in atomic beams in the discharge tube
experiments. It was considered a unit present in all other atoms.
ii. Earnest Rutherford (in 1919) proved the presence of proton in the nucleus. He bombarded
nitrogen and aluminium atoms with a particles. Protons were ejected. As neutrons are unstable
outside the nucleus, they disintegrate into proton and electron.
iii. Protons were obtained in numerous nuclear reactions. This confirms that all atoms contain
protons.
Q.21. Define a proton.
Ans: i. A proton is defined as a subatomic particle which has a mass of 1.00727 amu and a charge
of +1 elementary charge unit.
ii. It has unit mass and unit positive charge.

3.4 : Discovery of neutrons and constitution of atomic nucleus :

Q.22. Give an account of Prout's theory. Why was it rejected?
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Ans: i. Earlier only protons and electrons were 'known as constituent particles of an atom. They
were called subatomic particles.
ii. William Prout proposed that the atoms of the elements contain requisite number of
hydrogen atom units.
iii. Taking the atomic mass of hydrogen atom as 1.000, the atomic masses of all elements were
assumed to be whole numbers. Chlorine and copper had atomic masses 35.5 and 63.5
respectively. Hence Prout's theory was rejected.
Note:
Prout's theory was wrongly rejected as there was no knowledge of presence of two natural
isotopes of chlorine and copper at the time of rejection.
Q.23. Give an account of proton-electron theory? Why was it rejected?
Ans: i. According to Prout's theory, the nucleus of oxygen (atomic mass 16), should contain 16
protons and there should be 16 extranuclear electrons. Similarly, helium should contain 4
protons in the nucleus and 4 extranuclear electrons.
ii. However, oxygen, helium and almost all atoms of the elements contained almost half the
number of extranuclear electrons than the number predicted by Prout's theory.
iii. To account for the discrepancy, a new theory i.e., the proton-electron theory was
proposed. As per this theory, apart from extranuclear electrons, some electrons are also
present inside the nucleus.
iv. This was supported by the observed emission of P particle, i.e. electron from the nucleus.
v. Fermi rejected this theory, as it could not explain spin of some nuclei and energies of P
particles emitted by radioactive nuclei. Also electron cannot be accommodated in the small
space of atomic nucleus of size 10–15 due to its large size.
Q.24. Describe in brief the proposal of existence of the neutron in atoms.
Ans: i. Failure of Prout's theory, proton-electron theory in an attempt to suggest constituents of
an atom led to the proposal of the existence of the neutron.
ii. In order to overcome the failure of the proton-electron theory, Rutherford, in 1920,
proposed the existence of a neutral particle made from a combination of proton and
electron. He named it neutron. It has no charge and has mass almost equal to the mass of
the proton.
iii. As it satisfied all characteristics of atomic nucleus like mass, charge, spin it was accepted
by all.
iv. Neutron remained a hypothetical particle for sometime, as it could not be deflected in
electric and magnetic field.