UNIT-2

ATOMIC STRUCTUR
The conccpt of atom was first introduccd by Joln Dalton in 1808. His theory called "Dallon's
atomic the ory" regarded atom as the smallet ndivisible particle of matter.
Later at the end of 19h cent-1ry thc experimental evidences obtained by scientists like J.J
Thomson, Rutherford, Chahvick and many ohers proved the internal structure of atom. They found that
atoms are made up of fundamental particles like clectrons, protons and neutrons.
Discovery of clectrons - Cathode rays

The information about electrons was obtained fron the study of cathode rays. Cathode rays were
obtained by discharge tube experiments done by scientists mainly Faraday in mid 1850s.
Discharge tube is a long glass tube fitled with two mctal clectrodes on either cnds. The tube is also
connected to a vacuum pump for controlling the pressure of the gas inside the tube.

Gases are poor conductors of electricity To VACUUM

PUMP
under ordinary pressure. However, if a high
voltage (10000 volts) is applied under low GAS AI LOW PRESSURE

pressure, they become conducting. Also a st cam CATHODE ANODE

of particles starts moving in the tube from cathode
to anode. Since these rays originated from the
cathode, these rays are called cathode rays.
J.J. Thomson studied the nature and
properties of these rays. He found that these rays
consist of negatively charged particles. He called
HIGH VOLTA GE
them electrons.
Results of discharge tube experiment [Properties of cathode rays].
1, Cathode rays start from cathode and move towards anode.
2. In ihe absence of electric and magnetic felds,; çathode rays travel in straight line.
3. They can rotate light paddle wheel placed in their path. This shows that cathode rays consist of
material particles, which can produce mechanical motion.
4 They are deflected towards positive plate in an elecaric field. This shows that cathode rays consist
of negatively charged particles.
5 They are also defected in a magnetic field.
6 They prcduce fluorescence when falls on certain fluorescent or phosphorescent materials.
7. Cathode ray ionizes the gases through which they pass.
They produce X-rays when fall on metals such as tungsten, copper ctc.
The charge and mass of the particles in the cathode ray is
independent of the nature of the gas
iiisideilic tube. Tiüs we can coiicluda th£t ¿lectrois aie bäsii iÜistituciit üf all he
aiulis.
Clhargeto n:ssraiio (c/m) of electrons
The charye to nass (e/n) ratio for electrorn was determined by J.J Thomson. The value of e/m was
found to be !.758 xI0 coulombs/g (I.758 x 10' coulombs kg)
He deternined the e/n ratio by using cathode ray tubc ny
apptying cleciricziand nagnctic fields
perpendicuiar to the path of clectrons. The deviation of particles iro:u he path depcds o:a the tollowing
ctors.
-!.harge on the particle: Greater th charge, greater is he deleetion.
R Tihe ss of the particle: Lighter the particle, greiter is tht
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10"Hz) ’ Itis only part which our eyes can see or detect.

INCAEASING WAVE LENGTH

-DECREASING FREOUENCY
A(cm.) 1o-14 10 10 10 10 10 10 10
COSMIC rays X-rays ULTA Y INFRA MICAO AADIO
RAYS VMOLET RED WAVES WAVES

v(sec"')
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VIOLET BLUE GAEENYELLOW ORANGE AEO

3800 4300 4500 4900 $500 S900 6500 7600A

Limitation of wave theory of radiation

The wave theory was successful in explaining phenomena such as interference, diffraction etc. But
it failed to explain the following phenomena:
Black body radiation
Photoelectric effect
3. The variation of heat capacity of solids as a function of temperature.
4. Line spectra of atoms with special reference to hydrogen.

(a) Black body radiations:

The ideal body, which emits and absorbs radiations of all frequencies is called a black body. The
radiation emitted by such a body is called black body radiation.

When a black body is heated it becomes red hot. If

the temperature is further increased, the colour changes from T>T,
red to yellow to white and finally blue. This means that the
frequency of emitted radiation increases with increase in
temperature. [ Red colour lower frequenc. Blue colour
Higher frequency].
The intensity versus frequency of radiation from a
black body is given below. The frequency of emitted
radiation depends only on temperature. At 2 given
temperature, intensity increases with decrease of wavelength.
raches a nnaxiunn and thei starts decrrasing 1030 2000 3000
Wavelcngth (um)
This observation could not be explained by wave
theory Wavelength-intensity relattonsthip

P'age ?
 (b) Photoelectric eflcct: (H. Herl
The phenomenon of cjection of electrons fom the
surface of certain metals (eg: K, Rb, Cesium) when light of
suitable frequency strikes on it is calledphotoclectrice eflect.
The electrons ejected are called photoelectrons. The important
observations about photoelectric effect are:
(1) The electrons are ejected from the metal surface as
soon as the beanm of light strikes the surface.
(2) Only light of certain minimun1 frequency can cause
the photoelectric effect fivm a particular metal. That
frequency iscalled threshold frequency(u)
(3) radiation.
The kinetichutenergy of 4he photeelecirons is directly proportional tothe frequency of the incident
is independent of its intensity.
(4) incident
The number of photoelectrons emitted per second is directly proportional to the intensity of the
radiation.
These observations could not be explained by wave theory. According to wave theory light of any
frequercy can be made to have suficient, energy to cause emission of electrons by increasing its intensity.
Moreover the kinetic energy of ejected electron should be proportional to the intensity of light.
Particle nature of radlatiua Plnk's quanLn (lhcuryl
Particle nature of radiation is guided by the Plank'squantum theory proposed by Max Plank. The
main points of the theory are,
1. The radiant energy is emitted or absorbed discontinuously in the form of small packets of energy
called quantum. In the case light these particles are called photons.
2. The energy of each quantum is directy proportional to the frequency of the radiation.
Eov or E=hv or

Where 'h' is a constant called Plank's constant. Its value is 6.626 x 10 Js.
3. Abody can emit or absorb energy only in terms of the integral multiples of quantum.
E-nhv Where n = 1,2,3,--
Both black body radiation and photoelectric effect can be successfuily explained by Plank's theory.

() Explanation for Black body radiation:

When a black body is heated continuously, it undergoes a series of colour changes. This is because
when energy is supplied in theform of heat, it brings about change in its frequency (E ov). Since there is
a direct co-relation between colour and frequency, the colour change on heating can be justified.
(2) ExpBanation for photoelectric effect:
(alPhotoelectric effect can be explained on the basis of particle nature of ight. According to it,
light is a sream of photons. Each photon is a source of energy (E -hu ). The electrons are held to the metal
atom by certain force calfed binding energy. To overcome these forces certain minimum amount of energy
is required. This minimum energy is known as iÁreshold energy or work function. [E=hu').Therefore
to cause ejection of electrons the photon of incidert light should have energy equal to or greater than the
threshold energy (work function). if the energy of the incident photons are higher than the threshold
energy, the extra energy is taken up by the elearons that are ejecied as kinetic energy.
Energy of incident photon (hu) = ork funcion (h) + Kinetic Energy

Page &
 hu = hu +

= hu - hu

hu -u)
= hcf 1/- 1/2]
hus tor causing photoclectric effect, light of certain minimum frequency is required. Also
ncreasing the frequency of radiation increases the velocity (or kinetic energy) of electrons.
(b) An intense beam of light consists of larger no of photons. Consequently the no electrons
ejected is also larger. Therefore the number of photoclectrons emitted per second is directly proportinal to
the intensity of incident light.

Dual natureof radiation

Dual nature of radiation (light) was proposed by Einstein in 1905. Some characteristics of light
such as interfereme, difraction etc are explainsd only by the wave nature. But some other properties like
black body radiation, photoelectric efect etc can be explained only by particle nature of light. So it can be
suggested that light can behave as particles as well as wave. Einstein even calculated the mass of a photon
associated with a radiation of frequency 'u' as given below.

Energy E of the photon E = hu ----(1)

According to Einstein's equation, E = me ----(2) where 'm' is the mass of photon.
From equations (1) and (2), we get
hu = mc
hc/h = mc

m=
c
This equation can be used to calculate the mass of the photon.

Atomic spectrum
When a beam of light is passed through a prism, it splits up into seven colours (VBGYOR). This
passing through a
phenomenon of splitting of a beam of light into radiation of different frequencies by
spectrum.
prism is called dispersion. The pattern of radiation obtained after dispersion is called
from violet to red without any
In the spectrum obtained from white light, the colours change
discontinuity. This means that each colour merges into the other. Such a spectrum is called coztinuous
spectruL,
discharge etc, the atorns of the eicrnent
When an clernent is excited by heating, by passing elecric
radiations in the increasing order of wavelength
emit electronnagnetic radiations. The arrangement of these
Since these radiations are emitted due to energy changes taking
is called emission spectrun of the eiement.
place in the atoms, it is also known as atomic specrum.
by derk bends. That is they do
The atoiie specitra sf the elements consist cf bright ines separated spectrar. The various lines in
is cailed ine
not show a continaous spread of wavclengths. Such spectrun1
wavelengt!hs.
the spectrum correspond to the radiaticns of different

Page9
 are characteristic of the atoms of the
element.
The lines in the line spectrum of an element identify the element., Hence atomic spectrum is
Therefore the atonnic spectrum of an element can be used to
sometimes called fingerprint of atoms.

Absorption spectrun
light is passed through vapours or
An absorption spectrum is obtained when a beam of continuous spectroscope. The spectrum thus
a solution of a substance and the transmitted light is analyzed in absorption of radiation of
obtained contains a number of dark lines. These dark lines- appear due to the
corresponding wavelengths by the substance. The dark lines in the absorption spectrum of the substance,
as the bright line in the emission spectrum of the substance.
appear at the same position

SpectroscopY
The study of emission or absorption spectra is referred to as spectroscopy.

Hydrogen spectrum
When an electric discharge is passed through hydrogen gas in a discharge tube at low pressuure,
emit electromagnetic radiations
its molecules dissociate into hydrogen atoms. The excited hydrogen atoms
of discrete frequencies. The emitted light is then analyzed with a spectroscope.of lines. These series of lines
The spectru:n of hydrogen thus obtained consists of several series and
are present in ultraviolet, visible
are named after their discoverers. The lines of hydrogen spectrum
infra-red regions.
The five different series of lines in the hydrogen spectrum are
1. Liman series Ultraviolet region
Balmer series Visible region
3. Paschen series
4. Brackett series Infra-red region LINE
SPECTRUM
Pfund series.

SLI

PAISM

OIsCHARGE TURE FILM

(CONTAINING
HYOROGEN
Enission spectrun of hydrogen..
lines in the
the spectral fines are expressed in terms of wave number, the
Balmer showed that when
the formula
visible region (Balmer series ) obey

Cm! Where n=3,4,5,...

V=)
hydrogen spectrum
formula which is applicable for all the series in the
Then Rydberg gave a general
Cm
v=109,677

Page 10
Where n, and n, are integers.
For
LYMAN 8ALMER PASCHCN 92ACKE?I PFL-NO
Lyman series, n = 2,3,4 ... SERIES SERiES sEAIES SEFIES sEPIES
Balmer series n, =2 n2 = 3,4,5....
Paschen series n =3 n2 = 4,5,6 ....
Brackett series n =4 n2 = 5,6,7 ...
Pfund series n =6,7,8..
Bohr model of atom Atomic syectrum of hydrogen.

Niels Bohr in 1913 proposed his aton model. The main points of this model are
1. The electrons in atom are revolving around the nucleus only in certain selected circular orbits.
These orbits are associated with definíte energies and are called energy shells or energy levels. These
are numbered as 1,2,3,4 etc and are designated as K,L,M,N....
2. The energy of an electron in an orbit does not change
with time. This means that energy of an electron in a 4 or N

particular orbit remains constant, That is why these 3 or M

orbits are also called stationary orbits. 2 or L

1 or K
3. The electron can move only in those orbit for which its
-NUCLEU3
angular momentum is an integral multiple of h/2T
(where h is the Planck's constant)
Angular momentum of the electron, Bohr's orbits.
mvr = nh/2 where n = 1,2,3...
In other words, angular momentum of electrons in an
atom is quantised. This indicates that only certain fixed
orbits are allowed.
4 energy level to higher energy
When energy is supplied to the electron, it may jump from lowerjumps back to the lower energy
level by absorbing a definite amount of energy. When the electronradiation.
of
level, it radiates same amount of energy in the form of photons

AE = E -E = hu

This expression is commonly known as Bohr's frequency rule

Success of Bohr's model

) Bohr's model could explain the stability of an atom. from higher energy
According to Bohr's model an electron will lose energy oniy when it jumps same orbit without
If no lower energy level is vacant, it will remain in the
level to lower energy level.
losing energy. Hence it explain the stability of atom.
in a particular orbit of liydrogen.
2) Boiir's theory helped in calculating the energy of an elèctrongiven by
The energy of an electron in the n" orbit of hydrogen is

En=-R n=1,23,....

where R is called Rydberg coustant and its value is 2.18 X 10j

2.18x 10-3
En= J/atom
n'
3) Radius of orbits
Bohr also calculated the radius of cireular orbits in hydrogen atoms. The radius can be given by
the expression
T,= n'x52.9 pm Where n=1,2,3---..

The radius of first orbit of hydrogen is equal to 52.9 pm. This is also known as Bohr radius. As 'n'
increases the radius of the orbit increases.
4) Bohr model is also applicable ions such as He, L etc which like hydrogen atom contain one
electron. For them the equation for energy and radius áre

- 2.178 x10 -8 Z 2 Jlatom

E, =

I, = n(52.9)
Z
pm
Where Z is the atomic number For He*, Z=2 and for L Z=3]
5) It is also possible to calculate the velocity of electrons in the orbits. The velocity increases with nuclear
charge but decreases with principal quantum numbe.
6) Bohr's model could explain the atomic spectrum of
hydrogen.
According to Bohr model electron can have only certain definite energy levels. When energy is
absorbed by the atom, electron moves from a lower energy orbit to a higher energy orbit. Conversely when
energy (radiation) is emitted, electron moves from a higher energy orbit to a lower energy orbit.

Suppose an electron in an excited state with n = n, drops to a lower energy state with n=n,., The
difference in energies between two states is given by

AE = E, - Em
- 2.18 xl0 -!8
AE =

2.18 x10

E hu

2.18 x10 -8

6.626x10 s

Therefore 2.18 x10 -*

S
6.626 x 10*

In terms of wave nunber 2.18 xl0 n

6 626 x 10* x3i0

Page 12
 1.09677 x10" n

The above equation is same as the Rhydberg

equation deduced from experimental data.
Bohr's model also accounts for
large nunber of lines in hydrogen the existence of
spectrum.
case of large number of hydrogen atoms, In the
different
transitions are possible. This leads to large number Plund
of spectral lines. Brackett

The transitions of electrons from higher Paschen

energy levels to the first energy level are grouped Encrgy
together as Lyman series. The transitions of
electrons from higher energy levels to the second Balmer
energy level are grouped together as Balmer series.
Similarly transitions to the 3rd, 4h and 5h energy
levels give rise to Paschen, Brackett and Pfund
series respectively.
Lyman
Negative value of electronic energy

When an electron is at infinite distance from the nucleus, there is no force of attraction between
the electron and the nucleus. The energy of such an electron is arbitrarily assumed to be zero. When the
electron moves towards the nucleus, energy released due to force of attraction. Therefore the energy of
electron becomes less than zero. That is why energy of electron is negative.

Shortcomings of Bohr's model

Bohr's model has the following limitations.

1. Bohr's model could not explain the spectra of atoms containing more than one electron.
2. The model faiied to explain the fine structure of hydrogen spectrum. By using spectroscopes of
high resolving power, it is observed that each line of hydrogen spectrum splits in to two closely
spaced lines. This is known as the fine spectrum.
3. It is observed that in the presence of amagnetic field, each spectral line gets split up into closely
spaced lines. This phenomenon is known as Zeeman effect. Similarly the splitting of spectral lines
under an electric fieid is called Stark effect. These effects could not be explained by Bohr's
model.
4 It could not explain the ability of atoms to form molecules by chemical bonds.
5. de Broglie suggested that electron like light, has a dual character. (particle and wave character).
But Bohr had treated electron only as a particle.
6 Bohr model is contrary to Heisenberg's uncertainty principle.
Dual nature of matter - de Broglie Equation.

Louis de Broglie in 1924 postulated that natter, like radiation, should exhibit a dual behaviour ie
wave and particle nature. He derived a relationship betwecn the wavelength () of a material particBe, its
linear nmomentun (p) and planks constant (h)

The waves associated with particle in motion are called atter waves or de Broglie waves.
 Derivation for de Broglie Equation
de Broglie Equation has been derived initially for plhotons of
theory and Einstein's equation. light bascd on Planck's quantum
According to Planck's theory,
Energy of a photon, E= hu where u' is the frequency of light.
AccordingEnergy,
to Einsteine`s cquation,
E = mo
Comparing the above two equations,
hu = me
hc
me

hc
mc
For a particle having nass 'm' and
velocity v'

The above equation implies that

Similarly the wavelength of a particle heavier particles have shorter wavelength than
decreases as its velocity increases. lighter particles.
de Broglie's prediction was
undergoes diffraction. Diffräction is confirmed
a experimentally when it was found that an electron beam
electron microscope. Electron microscopephenomenon characteristic of waves. This principle is used in
is based on the wave like
behaviour of electrons.
de Broglie equation can be applied
atoms etc. It has no relevance for the only to the moving microscopic particles like electron, proton,
moving macroscopic partic!es. This is because for
particles such as a bullet or a ball, the de Broglie macroscopic
wavelength is so small and it cannot be measured.
Heisenberg uncertainty principBe
Heisenberguncertainty principle states that it is impossible determine simultaneously both the
position and momentum ofa microscopic particle like electron
with accuracy or certainty.
Mathematically, Ax. Ap > h4n
Where Ax is the uncertainty in position and Ap is the
But p= my
uncertainty in momentum.
åp = mAv
Therefore the above re!ation is Ax (m Av) > h4
Ax. Av> h4nm
le the position and velocity of a
microscopic particle cannot be determined with certainty.
Sigaificance of uncertainty psinciple
1. Heisenberg uncertainty principle rules out the
electron. The position and velocity of an objectexistence of definite paths or trajectories for an
fix its trajectory or path. If it is not possible to
determine accurately the position and velocity of a particle at any
to tix its trajectory. Hence the given instant, it is not possible
uncertainty
concept of probability (orbitals). principle replaced the concept of definite orbits by the

Fage 14
 2
The ettectforofmacroscopic
negligible Heisenberg uncertainty
objects. principle is significant only for microscopic objects and is
Reasons for the failure of theBohr Model
tn Bohr model electron is defiied as a charged paticle nnoving in a well defined circular orbit.
But according to de Broglie concept electron has duel character [wave and particle nature]. The wave
character of electron is not considered in Bohr model. Moreover the orbit in Bohr model is a clearly defined
path. But this path can be con1pletely defined only if both position and velocity of clectron are known at the
sametime. This is against Heisenberg's uncertainty principle.
Quantum mechanics
On the basis dual nature of matter and Hesenberg's uncertainty principle, Erwin Schrodinger
developed a new branch of science called Quantum mechanies. Schrodinger developed an atomic model
taking into account both the wave and particle nature of the electron. This is known as wave mechanical
model of aton.
Important features of quantum mechanical model of atom:
The important features of quantum mechanical model of atom are
1) The energy of electrons in atoms is quantized.(lt can have only certain specific values.)
2) The existence of quantized electronic energy levels is a direct result of the wave like properties of
electrons.
3) Both the exact position and velocity of an electron in an atom cannot be determined
simultaneously.
4) The atomic orbital is the wave function y for an electron in atom. Since many wave functions ar
possible for an electron, there are many atomic orbitals in an atom. In each orbital the electron has
a definite energy. An orbital cannot contain more than two electrons. Electrons are filled in these
orbitals in the order of increasing energy.
S) The probability of finding an electron at a point within an atom is proportional to the square of the
orbital wave function y' at that point.
Physical significance of y and y
Yrefers to the amplitude of the electron wave. It has no physical significance. However y is very
important. y gives the intensity of electron in the space around the nucleus of the atom. In other words y
gives the probability of finding an electron in a particular region around the nucleus. Thus y' is called
probability density and y is called probability amplitude.

Orbit and Orbital:

An orbit, as proposed by Bohr is a circular path around the nucleus in which an electron moves.

Anorbital on the other hand is a quantum mechanical concept An orbital may be defined as the
regional space around the nucleus where the probability of finding an electron is the maximum (90 to
95%).

The important differences between orbit and an orbital are:

Orbit Orbital
It is a well defined circular path 1 It is the region around the nucleus where the
around the nucleus probability of finding an electron is the
maximum.
2 Orbits are circular inshape 2 Orbital ihave different shapes. Eg: s-orbital is
spherical and p-orbital is dumb-bell shaped.
3. The maximum number of electrons 3. An orbital cannot accommodate more than
in an orbit is given by 2n* two electrons.
4. Orbits are non directional in 4 Orbta!s fexcept s-orbital) have directional
character. cherectr.

Pas,. 15
 Quantun Numbers:
Each atomic orbital in an atom, is designated by a set of three numbers known as quanlum
mumbers. These quantum numberS specily, size, shapè and orientation of the electron orbital. These are
principal quantum mumber (n), azimnthal quantum number () and magnetic quantum number (mi). These
follow irecily from solution of Shrodinger wave equation. In order to designate an electron an additional
quantum number called spin quantum number is also needed (spinquantunm nember). It specifies the spin
of the electrons.

) The Principal quantum number (n)

It is the most important quantum number since it tells the principal energy level or shell to which
an electron belongs. It also gives the average distance of the electron from the nucleus.
the size of the orbital. Thus it determines
is denoted by the letter, n'. It can have any integral values except
1,2,3,4,-, The principal energy levels are also designated by the letters K, L, M, N etc. Higherzero ie n=
the value
of n' the higher is the electronic energy. There are n orbitals in a shell. The
maximum number of
electrons in ashell is given by 2n',
(2) The angular momentum quantum nunnber or Azimmuthal
quantum number () or Subsidiary quantunn number:
This quantum number is related to the orbital angular momentum of the
by I. The orbital angular momentum of the electron is electron. This is denoted
given by
Orbital angular momentum =

The value of gives the sub level or sub-shell in which the

shape of the orbital. It can have all possible whole number valúes fromelectron
is located. It determines the
0 to n-l. The various sub-shells are
designatcd as s, p, d, f. depcnding upon the valuc of 'r.
Value of1' 3 4
Designation of sub-shell p d f

When n=1, I can have only one value. ie 0'. It means that the first energy
shell (s- sub-shell) level has only one sub
When n =2, can have two values, 0 and 1. It means that the second principal energy level has two
sub-shells.(s-sub-shell (2s) and p-sub-shell(2p)]
When n = 3, P can have three values, 0, I and 2. It means that the third
three sub-shells. (s-sub-shell (3s), p-sub-shell(3p) and d-sub-shell (3d)] principal energy level has
(3) The magnetic quantum nuinber (m,):

Magnetic quantum number specifies the different orientations of electron cloud in a

shell. The different orientations are called orbitals. It is denoted particular sub
by im. For a given value of , it can have
a!l integral values from -l to +tIthrough zero. Thus it
makes a total of
For = 0(s-sub-shel), m, can have only one value m=0. If means(2/+1) values.
that S-sub-shell has only one orbital.
For I=1(p sub-shell) m, can have 3 values -,0, +1. This implies that
For -2(d-sub-shell) m can have the values p-sub-shell has 3 orbitals.
-2,-1,0,+1,+2. Thus for d-sub-sthel there are five orbitals.
(4) The syin Quantum number(s):
The electron noving around the nucleus also rotates or spin
spin angular momentum. Spin angular momentum of the about its own axis. Therefore it has
electron is a vector quantity and can haye two
orientations relative to the chosen axis. These two orientations are
numbers 'm,.The spin quantum number can have only two values thatdisinguishedare +l/2
by the spin quantum
indicates ciockwise spin (1) and -1/2 indicates anticlockwise spin (). This and -1/2. The +1/2 value
only two clectrons ar d these electrons implies that an orbital can hold
sheuld have opposite spins.

Page 16
 (3-orbit

Shapes of atomic orbitals

r
The variation of y and y as a function of
for Is and 2s electron is shown in fig.

For ls orbital the probability density isthe

maximum at the nucleus and it decreases sharply as
distance increases. But for 2s orbital the probability
density first decreases sharply to zero and starts
maximum it
increasing. After approaching a small probability
region where the
again decreases. The node
simply
reduces to zero is called nodal surface or 3
[radial node].
In general ns orbital has (n-1) nodes.
orbital = I
Eg. Number of nodes for 2s
Number of nodes for 3s orbital = 2
space can be given by two
of orbitals or the representation of the variation of y in
The shapes
approaches. Boundary surface diagrams.
(1)Charge cloud diagrams and (2)
1.Charge cloud diagrams:
shown as a collection of dots. The density of dots in any region
Here the probability density y is in that region.
represents the electron probability density 2s orbitals is given below.
Charge cloud diagrams of Is and

(a

2.Boundary surface diagrams ls 2s

the shape of an orbital

In boundary surface diagrams,probability density that ls 2s
constant
is defined as a surface of of the probability of (a) Probability density plots of ls and
encloses some large fraction (90%) 2s atomic orbitals. The density of the
finding the electron dots represents the probabilty density
shape of of finding the electron in that regior.
According to this model an s-orbital has the of 'n' (b) Boundary surface diagram for ls
centered on the nucleus. As the value
aspherical shell increases.
and 2s orbitals.
increases the size of the spherical she!l

Boundary surface diagrams of p-orbitals are shown inThey fig. Each p-orbital is dumb-bell shaped. For
are designated as px, P, and p. Of these
p-orbitals there are3 possible orientations of electron cloud. along y-axis and z-axis respectively Fachp
p, are oriented
Px orbita! is oriented a!cng x-axis and, p, 2ndThese lobes are on either side of the plane that passes
through
orbital consists of two sections called lobes,
plane of zero probability called nodal plane. For p,
the nucleus. Thus the two lobes are separated by a
ZX and XY respectively.
orbital the nodal plane is YZ and for p, and p,, the iodal planes are

2), 2p
2p. 7.

Page 17
 Boundary surface diagrams of d-orbitals are shown in fig. There are five d-orbitals. These are
designated as dyy, dyz, dan, d and d,. Allthe five 3d-orbitals are equivalent in energy.
dy

Angular uodes
Besides the radial nodes,p and d atomic orbitals have zero probability planes passing through the
origin (nucleus). For example in case of p, orbital, XY plane is the nodal plane. For a d orbital there are
two nodal planes passing through the origin. These are called angular nodes. The total mumber of angular
nodes for an orbital is given by 1".

For an orbital
Total nunmber of radial nodes = n--1
Total number of angular nodes =l
Total number of nodes =n-1

Electronic configuration of elements:

The distribution of electrons of an atom in its various orbitals is calied its electronic configuration.
It is goverened by the following rules.

() Aufbau principle:
According to this rule, electrons in an atom are filled in orbitals in order of their increasing energies.
The order of increase of energy of orbitals can be calculated from the (n+l) rule. (Bohr's Bury's rule).
According to this rule
1. The orbital having lower (n+) value has lower
energy.
For example:
For 4 s orbital: nt/ = 4 +0 = 4
For 3 d orbital; nt! = 3+2 = 5
Since 4s orbital has lower (n +)value, it will fill
before 3d.
If two orbitals have the same (n+l) value, the one
with lower 'n' will be filled tirst.
For example:
For 2 p orbital; nt! 2+ i = 3
For 3 s orbital: n+ = 3+0 = 3
Since 2p-orbita! has lower value of 'n' it has
lower energy than s and it will be filled first.
 Some are notations.
2. romthe only
The 1l. order
theirof
Representation having electrons all numbers.
spins. The
represented Orbital Orbltal Degenerate
orbitals 3) 2)
more
the Hund's Pauli's order
Here
diagram example Forthe The same orbitals
drawnotation The with This This
examples It in
electronic energy.and
energies. rule exclusion
follows
bythe back orbitals
parallel ofrule principle which
the method.
orbitals method. of of
of electronic thstates
e
are:
direction having niaximum that lsthe
this This spins.
sub-shell principle <
are electronicconfiguration therefore that states
an energies
2s
method
that is can orbital
represented
of configuration same pairing <
be multiplicity that 2p
oNe F: sO: these they
are
<3s of
configuration neon of done energy
singly of can no orbitals
: 1s, ls, arrows. of are
ls", as cannotoneget in an elcctronsaccommodate two <3p
ls2s", are occupied.
ls
ls2s',
two degenerate
2s, boxes atom electrons increase
ways. called <4$
2s
2p,2s2, 2p,'2,
2p,", and is in <3d
written degenerate is
2p,2p, 2p,2p,2p2p,
, 2, 2p,2p. 2p, the orbitals. Moreover the two in as
2p,, (1oNe)is
about
ideaany orbitals <4p
an follows.
2p,1 electrons electrons
2p,? 2p,' by atom
filing <
orbitals. the of 5s
written can Thercfore
by singly same and <4d
arrows. of have
spinstheof as atomic Eg. subshell thesc
occupied <
1s 2px, the Sp
tthcy
The 2p°.2s orbitals electrons
2py same also
spins does
individual
electrons orbitals fill
and
of in not must set
2pz of in
the the must take have four tho
electrons increasing orbitals place same
have quantum
opposite
19 order.
are the until