Lecture-1

ATOMIC STRUCTURE,
QUANTUM THEORY AND
BOHR ATOM

*** TEXT
“Essentials of Physical Chemistry”
B. S. Bahl, G. D. Tuli and Arun Bahl,
24th ed. (1997), S. Chand & Company Ltd,
ISBN: 81-219-0546-X

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ATOMIC STRUCTURE

Landmarks in the evolution

of atomic structure are:

1805 Dalton’s atomic theory

1896 Thomson discovery of electron and proton
1909 Rutherford’s nuclear atom
1913 Bohr’s atomic model
1932 Chadwick’s discovery of neutron
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 Atomic Theory of Dalton: (1805)
(1) All matter is composed of tiny particles called
atom which can not be created, destroyed or
splitted.
(2) All atoms of any one element are identical,
have same mass and chemical properties.
(3) A compound is a type of matter composed of
atoms of two or more elements.
(4) A chemical reaction consists of rearranging
atoms from one combination to another.

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Dalton’s Contribution:

British Chemist John Dalton provided the

basic theory: all matter- whether element,
compound, or mixture- is composed of small
particles called atoms.

Limitations of Dalton’s Model:

(1) Atom can be divided into subatomic particle
namely electron, proton and neutron.
(2) All atoms of any elements are not identical,
have different mass and chemical properties.
This property is known as isotopes.
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Rutherford’s Model of Atom: (1909)
(1) Atom has a tiny dense center core or the
NUCLEUS, which contains practically the
entire mass of the atom, leaving rest of the
atom almost empty.
(2) The entire positive charge of the atom is
located on the nucleus, while electrons were
distributed in vacant space around it.
(3) The electrons were moving in orbits or
closed circular paths around the nucleus like
planets around the sun.
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Rutherford’s Model of Atom (contd.):

Rutherford’s
Atomic Model
Contribution of Rutherford’s model:

 Rutherford laid the foundation of the

model picture of atom.
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 Weakness of the Rutherford Atomic Model:

According to electromagnetic theory-

1. Newton’s Laws of motion and gravitation can only be
applied to neutral bodies such as planets and not to
charged bodies such as tiny electrons moving round a
positive nucleus.
2. If a charged particle accelerates around an oppositely
charged particle, the former will radiate energy.
3. If an electron radiates energy, its speed will decrease
and it will go into spiral motion, finally falling the
nucleus, which would make the atom unstable.
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 Three subatomic particles or principal
fundamental particles:

Mass Charge
Particle Symbol
amu grams Units Coloumbs

Electron e- 1/1835 9.110-28 -1 -1.610-19

Proton p+ 1 1.67210-24 +1 +1.610-19

Neutron N or no 1 1.67410-24 0 0

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 Atomic Number, Mass Number &
Isotopes
 An atom consists of three particles- electron,
proton and neutron. The charge of proton is
positive, electron is negative and neutron no
charge.
 In a neutral atom, number of proton is equal
to that of the electron and a proton has mass
more than 1800 times that of the electron.
 The neutron is a nuclear particle having a
mass almost identical to that of the proton.

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 Atomic number, Mass number
and Isotopes

Atomic number (Z) = number of protons in nucleus

Mass number (A) = number of protons + number of neutrons
= atomic number (Z) + number of neutrons
Isotopes are atoms of the same element (X) with different numbers
of neutrons in their nuclei

Mass Number A
ZX
Element Symbol
Atomic Number

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 The Isotopes of Hydrogen

1 2 3
1 H 1 H 1H
hydrogen deuterium tritium

235 238
92 U 92 U
12 13 14
6C 6C 6C 11
Quantum Theory and Bohr Atom:
(1913)

To understand the Bohr theory, we need to

learn-

 The nature of electromagnetic radiations

 The atomic spectra

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 Electromagnetic Radiations:
 Electromagnetic radiation can be described as a
wave (carrier of energy) occurring simultaneously
in electrical and magnetic fields and consists of
particles called quanta or photons.

 Energy can be transmitted through space by

electromagnetic radiations.

 Some forms of electromagnetic radiations are:

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 Electromagnetic Radiations (contd.)
 Radio waves
 Visible light
 Infrared light
 Ultraviolet light
 X-rays etc

These radiations have both the properties of a wave

as well as a particle, now become familiar for their
uses. The X-rays are used in medical treatment, the
ultraviolet rays lead to sunburns and radio and radar
waves used in communication and visible light.
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Electromagnetic radiations or waves…

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 Characteristics of Waves:

Figure: Illustration of wave motion caused by a vibrating source

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Wavelength (, lambda):
The wavelength is defined as the distance
between two successive crests or troughs
of a wave.
Units: cm, m or Å (angstrom).
(1 Å = 10-8 cm = 10-10 m, 1 nm = 10-9 m)

Frequency (, nu):

The frequency is the number of waves

which pass a given point in one second.
Units: hertz (hz), one cycle per second.
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A wave of high frequency has a shorter wavelength,
while a wave of low frequency has a longer
wavelength.

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Speed (c):
The speed (or velocity) of a wave is the
distance through which a particular wave
travels in one second.
Speed = Frequency  Wavelength
i. e. c =   

Wave Number:
This is reciprocal of the wavelength and is
given the symbol (nu bar). i. e.  = 1/
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Problems:
1# The wavelength of a violet light is 400
nm. Calculate its frequency and wave
number. (Given, c = 3×108m sec-1) (Answer:
 = 7.5 × 1014 sec-1,  = 25 × 105 m-1)

2# The frequency of a strong yellow line

in the spectrum of sodium is 5.09  1014
sec-1. Calculate the wavelength of light in
nanometers. (Answer:  = 589 nm)
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Solution 1:

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Solution 2:

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Spectra:
A spectrum is an arrangement of
waves or particles spread out
according to the increasing or
decreasing of some property like
wavelength or frequency.

An increase in frequency or a decrease in

wavelength represents an increase in energy.

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Continuous Spectrum:
White light is radiant energy coming from the sun or
from incandescent lamps. It is composed of light
waves in the range 4000-8000 Å.

Figure: The continuous spectrum of white light. 24

When a beam of white light is passed through a
prism, a continuous series of colour bands (rainbow)
is received on a screen with different wavelengths
called Continuous Spectrum.

VIBGYOR - Violet
 - Indigo
 - Blue
 - Green
 - Yellow
 - Orange and
 - Red 25
 The violet component of the spectrum has
shorter wavelengths (4000-4250Å) and higher
frequencies.
 The red component has longer wavelengths
(6500-7500Å) and lower frequencies.
 The invisible region beyond the violet is
called ultraviolet region and the one below the
red is called infrared region 26
 Atomic Spectra:
 When an element in the vapor or the gaseous state is
heated in a flame or a discharge tube, the atoms are
excited and emit light radiations of a characteristic
colour. The cooler of light produced indicates the
wavelength of the radiation emitted.
For example, a Bunsen burner flame is coloured yellow by
sodium salts, and violet by potassium.
 The spectrum obtained on the photographic plate is
found to consists of bright lines.
 Such a spectrum in which each line represents a specific
wavelength of radiation emitted by the atoms is referred
to as the Atomic Emission spectrum of the element.
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 Atomic Spectra:
Emission spectra of K, Na, Li and H

An individual line of these spectra is called a Spectral line. 28

 Atomic Spectrum of Hydrogen:

In 1884 J. J. Balmer observed the following four

prominent coloured lines in the visible hydrogen
spectrum:
(1) a red line with a wavelength of 6563 Å
(2) a blue-green line with a wavelength of 4861 Å
(3) a blue line with a wavelength of 4340 Å
(4) a violet line with a wavelength of 4102 Å

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The series of four lines in the visible spectrum of
hydrogen is known as Balmer series.

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 Balmer equation:
Balmer was able to give an equation which
relate the wavelengh () of the observed
lines. The Balmer equation is,
1  1 1 
R  2  2 
 2 n 
where R is a constant called Rydberg
constant which has the value 109, 677 cm -1
and n = 3, 4, 5, 6, etc.
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Five Spectral Series:
In addition to Balmer series, four other spectral
series were discovered in the infrared (ir) and
ultraviolet (uv) regions of the hydrogen
spectrum. These bear the names of discoverers.
(1) Lyman series (uv)
(2) Balmer series (visible)
(3) Paschen series (ir)
(4) Brackett series (ir)
(5) Pfund series (ir)
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 Quantum Theory of Radiation
(1) When atoms or molecules absorb or emit
radiant energy, they do so in separate ‘units of
waves’ called quanta or photons.
Thus light radiations obtained from energised
or ‘excited atoms’ consist of a stream of photons and
not continuous waves.

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Figure: A continuous wave and photons.
 Quantum Theory of Radiation (contd.):
(2) The energy, E, of a quantum or photon
is given by the relation.
E = h (h, Planck’s constant
= 6.62  10–27 erg sec.
or 6.62  10-34 J sec.)
and  is the frequency of the emitted radiation
We know that, velocity of radiation c = 
hc
E 

Thus the magnitude of a quantum or photon of energy is
directly proportional to the frequency of the radiant energy, or
is inversely proportional to its wavelength, λ. 34
Quantum Theory of Radiation (contd.):
(3) An atom or molecule can emit (or
absorb) either one quantum of energy
(h) or any whole number multiple of this unit.
- Thus radiant energy can be emitted as hν, 2hν,
3hν, and so on, but never as 1.5 hν, 3.27 hν, 5.9 hν,
or any other fractional value of hν i.e. nhν
- Quantum theory provided admirably a basis for
explaining the photoelectric effect, atomic spectra
and also helped in understanding the modern
concepts of atomic and molecular structure.

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BOHR MODEL OF THE ATOM
1. Electrons travel around the nucleus in
specific permitted circular orbits and in
no others.
2. While in these specific orbits, an
electron does not radiate (or lose)
energy.
3. An electron can move from one
energy level to another by quantum or
photon jumps only.

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 Bohr Model of the Atom (contd.):
Electrons
Nucleus not allowed
between orbits

Electrons
permitted in
circular orbits 1
2
3
4
Orbit Nos
Figure: Circular electron orbits or
stationary energy levels in an atom 37
Bohr Model of the Atom (contd.):
4. The angular momentum (mvr) of an
electron orbiting around the nucleus is an
integral multiple of Planck’s constant
divided by 2.
nh
 mvr 
2
where m = mass of electron,
v = velocity of electron,
r = radius of the orbit,
n = 1, 2, 3…..etc and
h = Planck’s constant.
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Calculation of Radius of Orbits:

Consider, an electron of mv 2
charge e revolving r
around a nucleus of v Force of
e Attraction
charge Ze, where Z is the
atomic number and e the r

charge on a proton. Let

Ze
m be the mass of the
electron, r the radius of
the orbit and v the
Fig. Forces keeping
tangential velocity of the
electron in orbit
revolving electron.
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Calculation of Radius of Orbits (cont.):

The electrostatic force of attraction between the nucleus

and the electron (Coulomb’s law),

The centrifugal force acting on the electron

Bohr assumed that these two opposing forces must be

balancing each other exactly to keep the electron in orbit.
Thus,

For hydrogen Z = 1, therefore, - ------ (1)

Multiplying both sides by r ------ (2)

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41
Energy of electron in each orbit:

(Hints: P.E.=kq1q2/r; attractive force, so negative)

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Energy of electron in each orbit (cont):

(Since the value of h, m and e had

been determined experimentally)

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 Problems:
 Problem-3: Calculate the first five Bohr
radii of the hydrogen atom.
 Problem-4: Calculate the radius of the third
orbit of hydrogen atom.
 Problem-5: Calculate the five lowest
energy levels of the hydrogen atom.
 Problem-6: Calculate the energy of electron
of the second orbit of the hydrogen atom.

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Solution 3:

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Solution 5:

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Bohr Explanation of Hydrogen Spectrum:
 The solitary electron in hydrogen atom at ordinary
temperature resides in the first orbit (n =1) and is in
the lowest energy state (ground state).
 When energy is supplied to hydrogen gas in the
discharge tube, the electron moves to higher energy
levels viz., 2, 3, 4, 5, etc., depending on the quantity
of energy absorbed.
 From these high energy levels, the electron returns
by jumps to one or other lower energy level. In doing
so the electron emits the excess energy as a photon.
 This gives an excellent explanation of the various
spectral series of hydrogen.

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Lyman series is obtained when the electron
returns to the ground state i.e., n = 1 from
higher levels (n2 = 2, 3, 4, 5, etc.).

Similarly, Balmer, Paschen, Brackett and

Pfund series are produced when the electron
returns to the second, third, fourth and fifth
energy levels respectively as shown in figure
below:

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Hydrogen spectral series:
7
6
5
PFUND SERIES
4
BRACKETT SERIES

3
PASCHEN SERIES

2
BALMER SERIES

ENERGY
LEVELS

GROUND STATE
1
LYMAN SERIES

FIGURE. Hydrogen spectral series on a Bohr atom energy diagram.

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 Table: Spectral series of hydrogen
Series n1 n2 Region Wavelength 
(Å)
Lyman 1 2, 3, 4, 5, etc. Ultraviolet 920-1200

Balmer 2 3, 4, 5, 6, etc. Visible 4000-6500

Paschen 3 4, 5, 6, 7, etc. Infrared 9500-18750

Brackett 4 5, 6, 7 Infrared 19450-40500

Pfund 5 6, 7 Infrared 37800-75000

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Shortcoming of the Bohr Atom:
 It is unsuccessful for every other atom
containing more than one electron.
 In view of modern advances, like dual nature of
matter, uncertainty principle etc. any mechanical
model of the atom stands rejected.
 Bohr’s model of electronic structure could not
account for the ability of atoms to form
molecules through chemical bonds.
 Bohr’s theory could not explain the effect of
magnetic field (Zeeman effect) and electric field
(Stark effect) on the spectra of atoms.
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 1 =
 1 1 
R  2  2 
Questions:   n1 n2 
1. Explain- ‘values of Rydberg’s
constant is the same as in the original
empirical Balmer’s equation’.
2. How do you calculate the
wavelengths of the spectral lines of
hydrogen in the visible region using
Balmer equation?

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 Problems:
Problem-7: Calculate the wavelength in Å of the line in
Balmer series that is associated with drop of the electron
from the fourth orbit. The value of Rydberg constant is
109,676 cm-1.
Problem-8: Calculate the wavelength in Å of the third line in
Balmer series that is associated with drop of the electron.
(Rydberg constant =109,676 cm-1).
Problem-9: The energy of the electron in the second and
third orbits of the hydrogen atom is -5.42 ×10-12 erg and -
2.41×10-12 erg respectively. Calculate the wave length of the
emitted radiation when the electron drops from third to
second orbit. (Answer: 6600Å)
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Solution 7:

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 next class
QUIZ-1

Thank you
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