Atomic structure

An atom is defined as the smallest unit of the matter, which retains all the chemical

properties of an element. Atoms combine to form molecules, which interact to form

different phases like solid, liquid or gases. For example carbon dioxide is made up

of carbon and oxygen atom, which combines together to form carbon dioxide

molecule. An atom may or may not be capable of independent existence. For

example atoms of Iron, Copper, and Gold etc. can exist freely where as atom of

Hydrogen, Oxygen, Nitrogen etc. cannot exist freely. They exist as H2 O2 N2 etc.

An atom is composed of two regions, the nucleus which is the center of the atom

and contains protons and neutrons and the outer region of the atom, which hold

its electron in orbit around the nucleus

Electron
An electron is that fundamental particle which carries one unit negative charge

and has a mass nearly equal to 1/1837 of that of hydrogen atom

Proton

A proton may be defined as those fundamental particles which carries one unit

positive charge and has a mass nearly equal to that of hydrogen atom.

Neutron

a neutron may be defined as that fundamental particle which carries no charge

but has a mass nearly equal to that of hydrogen atom or proton

Protons and neutrons have approximately the same mass about 1.67x10-24 grams

which scientists define as one atomic mass unit (amu) or one Dalton

Charges and mass of fundamental subatomic particles

Particles Charge Mass

(Discoverer) Kg u
Electron -1 9.10939 x 10-31 0.000548596
(J. J. Thomson)
Proton +1 1.67262 x 10-27 1.00727663
(Goldstein)
Neutron 0 1.67493 x 10-27 1.0086654
(Chadwick)
Atomic number and Mass number

Since the atom as a whole is electrically neutral therefore the number of positively

charged particles i.e., protons present in the atom must be equal to the number of

negative charged particles i.e., electrons present in it. This number is called

atomic number

Hence

Atomic number of element

= Total number of protons present in the nucleus

= Total number of electrons present in the neutral atom

Atomic number is also known as proton numbers because the charge on the

nucleus depends upon the number of protons

Since the electrons have negligible mass the entire mass of the atom is mainly

due to protons and neutrons only. Since these particles are present in the nucleus

therefore they are collectively called nucleons.

As each of these particles has one unit mass on the atomic mass scale therefore

the sum of the number of protons and neutrons will be nearly equal to the mass of

the atom. This is called mass number

Therefore mass number of an element = number of proton + number of neutrons

The atomic number (Z) and the mass number (A) of an element X are usually

represented along with the symbol of the element

For example , etc.

Isotopes, Isobars, Isotones and Isoelectronics

Isotopes

In some cases atoms of the same element are found to contain the same number

of protons but different number of neutrons.As a result they have the same atomic

number but different mass number

Such atoms of the same element having same atomic number but different mass

number are called isotopes

For example

Three isotopes of Hydrogen

Protium: Deuterium: and Tritium

Two isotopes of chlorine: and

Isobars

Some atoms of different elements which have the same mass number (and of

course different atomic number) are called isobars.

For example: , and

Isotones

It may be noted that isotopes differ in the number of neutrons only whereas isobars

differ in the number of neutrons as well as protons however some atoms of

different elements are found to have the same number of neutrons

Such atoms of different elements which contain the same number of neutrons are

called isotones.

For example: , and

Isoelectronics

The species (atoms or ions) containing the same numbers of electrons are called

isoelectronic

For example: O2-, F-, Na+, Mg2+, Al3+ and Ne

Each of them contain 10 electrons is and hence they are isoelectronics.

Bohr's model of atom

The main postulates of Bohr's model of atom are as follows

1. An atom consists of small heavy positive charged nucleus in the center and

electrons revolve around it in a circular path.

2. Out of large number of circular orbits theoretically possible around the nucleus

the electrons revolve only in those orbits, which have a fixed value of energy.

Hence these orbits are called energy level or stationary states.

The stationary states mean that energy of the electrons revolving in a particular

orbit is fixed and does not change with time.

The different energy levels are number as 1, 2, 3, 4..etc. or designated as K, L, M,

N, O, P ……. etc. starting from the shell closed to the nucleus.

a) The energies of the different stationery states in case of hydrogen atom are

given by the expression (called Bohr formula)

En = - 22me4/n2h2

Substituting the value of m (mass of the electron charge), c(charge on the

electron) and h (plank’s constant) we get

En = - 21.8 x 10-19/n2 J/atom

= 13.6/n2eV/atom {1eV = 1.6022 x 10-19J}

= - 1312/n2 kJ mol-1

Where n = 1, 2, 3 ……… etc. stand for 1st, 2nd, 3rd… etc. level respectively

Thus, the 1stenergy level (n =1), which is closed to the nucleus, has lowest energy

The energy of the level increases as we move (outwards) from the 1stlevel (K level)

Thus the energies of the various level are in the order

1st< 2nd< 3rd< 4th …………… and so on.

or

K < L < M < N …………… and so on.

For hydrogen like particle, e.g. He+, Li2+ (containing one electron) the expression

for the energy is

En = -22me4Z2/n2h2

= - 1312 Z2/n2 kJ mol-1

Where Z is the atomic number of the element

For, He+, Z = 2

Li2+, Z = 3

b) The radii of the stationary states of the hydrogen atom are given by the

expression

rn = a02

Where a0 = 52.9 pm is the radius of the first stationary state and is called Bohr’s

radius.

For hydrogen like particles, the radii of the stationary states are given by the

expression

rn = a0n2/Z

c) The velocities of the electrons in the different orbit are given by the expression
Vn = V0Z/n

Where V0 = 2.188 x 108 cms-1 is the velocity of the electron in the first orbit of

hydrogen atom.

3) Since the electron revolve only in those orbits which have fixed values of

energy, hence electrons in an atom can have only certain definite values of energy

and not any value of their own.

This is expressed by saying that the energy of the electron is quantized.

4) Like energy, the angular momentum of an electron in an atom can have certain

definite or discrete value and not any value of its own.

The only permissible value of angular momentum are given by the expression

mvr = nh/2

i.e., angular momentum of the electron is an integral multiple of h/2

Here, m is the mass of the electron v is the tangential velocity of the revolving

electron, r is the radius of the orbit, and h is the Planck’s constant and n is any

integer.

In other words the angular momentum of the electron can be h/2, 2h/2,

3h/2,……… etc. This means that like energy, the angular momentum of an

electron in an atom is also quantized.

5) When the electron in an atom are in their lowest (normal) energy states, they

keep on revolving in their respective orbits without losing energy because energy

can neither be lost nor gained continuously. This state of atom is called normal or

ground state.

6) Energy is emitted or absorb only when the electrons jumps from one orbit to the

other. For example, when energy is supplied to an atom by subjecting it to

electrical discharge or high temperature, and electron in the atom may jump from

its normal energy level (ground state) to some higher energy level by absorbing a

definite amount of energy. This state of atom is called excited state.

Since the lifetime of the electron in the excited state is short, it immediately jumps

back to lower energy level by emitting energy in the form of light of suitable

frequency or wavelength.

The amount of energy emitted or absorbed is given by the difference of energies

of the two energy levels concerned, i.e.

∆E = E2 – E1

Where E2 and E1are the energies of the electron in the higher and lower energy

levels respectively and ∆E is the difference in energies of the two levels.

Further, since each energy level is associated with a certain definite amount of

energy, therefore energy is always emitted or absorbed in certain discrete

quantities is called quanta’s or photons and not any value. This means that the

energy of the electron cannot change gradually and continuously but changes

abruptly as the electron jumps from one energy level to the other.
Advantages of Bohr’s model

The main advantages of Bohr’s models are as under:

1) It explains the stability of the atom.

According to Bohr's theory, an electron cannot lose energy as long as it stays in a

particular orbit. Therefore the question of losing energy continuously and falling

into the nucleus does not arise.

2) It explains the line spectrum of hydrogen.

The most remarkable success of the Bohr’s theory is that it provides a satisfactory

explanation for the line spectrum of hydrogen.

According to Bohr’s theory, an electron neither emits not absorbs energy as long

as it stays in a particular orbit. However, when an atom is subjected to electric

discharge or high temperature, an electron in the atom may jump from the normal

energy level (ground state) to some higher energy level (excited state).

Since the lifetime of the electron in the excited states is short, it returns to some

lower energy level or even to the ground state in one or more jumps. During each

such jump, energy is emitted in the form of a photon of light of a definite

wavelength or frequency.

The frequency (ѵ) of the photon of light thus emitted depends upon the energy

difference of the two energy levels concerned and is given by the expression

E2 – E1 = hѵ
or

ѵ = E2 – E1 / h

Where E2 is energy of higher energy level and E1 is the energy of lower energy

level and h is the Planck’s constant.

Now frequency is related to the wavelength as ѵ = c / 

Where c is the velocity of light.

Therefore,

ѵ=c/

= E2 – E1 / h

or

 = hc / E2 – E1

Corresponding to the frequency or wavelength of each photon emitted, there

appears a lines in the spectrum. The frequencies (or wavelength) of the spectral

lines calculated with the help of above equations are found to be very in good

agreement with the experimental values.

Thus, Bohr’s theory explains the line spectrum of hydrogen and hydrogen like

particles (like He+, Li2+, Be3+ etc.)

Line Spectrum of Hydrogen

Although an atom of hydrogen contains only one electron, yet its atomic spectrum

consists of a large number of lines which have been grouped into five series, i.e.
Lyman, Balmer, Paschen, Brackett and Pfund. This may be explained as

follows:

Any given sample of hydrogen gas contains a large number of molecules. When

such a sample is heated to a high temperature or an electric discharge is passed,

the hydrogen molecules split in two hydrogen atoms. The electrons in different

hydrogen atoms absorb different amounts of energies and are excited to different

energy levels. For example, the electrons in some atoms are excited to second

energy level (L), while in others they may be promoted to third (M), fourth (N), fifth

(O) energy levels and so on. Since the lifetime of the electrons in this excited

states is very small, they returned to some lower energy level or even to ground

states in one or more jumps. Thus, different excited electrons adopted

different routes to returns to various lower energy levels or the ground state. As a

result, they emit different amounts of energy and thus produce a large number of

lines in the atomic spectrum of hydrogen.

The various possibilities by which the electrons jumps back from various excited

states are shown in figure below.

For example, when the electron jumps from energy levels higher than n = 1, i.e.,

n = 2, 3, 4, 5, 6…..etc. to n = 1 energy level, the group of lines produced is called

Lymen series. These lines lie in the ultraviolet region.

Similarly, the group of lines produced when electron jumps from 3rd, 4th, 5th or any

higher energy level to second energy level, is called Balmer series. These lines lie

in the visible region.

In a similar way, Paschen series is obtained by the electronic jumps from 4th, 5th

or any higher energy level to 3rd energy level. Similarly Brackett series results from

electronic transitions from 5th, 6th or any higher energy level to the 4th energy level.

Lastly, the Pfund series originates by electronic jump from 6th, 7th or any higher
level to 5th energy level. The spectrum lines of the last three series lie in the

infrared region.

To Sum up

Lyman Series: From n = 2, 3, 4………… to n = 1

Balmer Series: From n = 3, 4, 5 …………to n = 2

Paschen Series: From n = 4, 5, 6 …………to n = 3

Brackett Series: From n = 5, 6, 7………….to n = 4

Pfund Series: From n = 6, 7, 8 …………to n = 5

Limitations of Bohr's model of atom

Bohr’s model of atom suffers from the following limitations.

1) Inability to explain line spectra of multi-electron atoms.

Bohr's theory was successful in explaining the line spectra of hydrogen atom and

hydrogen like particles, containing single electron only. However, it failed to

explain the line spectra of multi electron atoms. When spectroscopes with better

resolving power were used, it was found that even in case of hydrogen spectrum

each line was split up into number of closely spaced line (called fine structure)

which could not be explained by Bohr’s model of atom.

2) Inability to explain splitting of lines in the magnetic field (Zeeman effect)

and in the electric field (Stark effect)

In the production of line spectrum, if the source emitting the radiation is placed in

a magnetic field or in an electric field, it is observed that each spectral line splits

up into a number of lines. This splitting of spectral lines in the magnetic field is

called Zeeman effect while the splitting of spectral line in the electric field is called

Stark effect. Bohr’s model of atom was unable to explain this splitting of spectral

lines.

3) Inability to explain the three-dimensional model of atom

According to Bohr's model of atom, the electrons move along certain circular path

in one plane. Thus it gives a flat model of atom. But now it is well established that

the atom is three dimensional and not flat, as had been suggested by the bohr.

4) Inability to explain the shape of molecules

Now it is well known that in covalent molecules, the bond have directional

characteristics (i.e., atoms are linked to each other in particular directions) and

hence they possess definite shapes. Bohr's model is unable to explain it.

5) Inability to explain the de Broglie concept of dual nature of matter and

Heisenberg’s uncertainty principle.

This theory was unable to explain the de Broglie concept of dual nature of matter

and Heisenberg’s uncertainty principle.

Dual nature of radiation

As we know that the photoelectric effect could be explained considering the

radiation consists of small packets of energy called quanta or quantum. These

packets of energy can be treated as particles.

On the other hand, radiation exhibits the phenomenon of interference and

diffraction which indicate that they possess wave nature.

So it may be concluded that radiation poses dual nature i.e. particle nature as well

as wave nature.

Einstein (1905) even calculated the mass of the photon associated with the

radiation of frequency ѵ.

The energy E of photon is given as E = hѵ ……………. 1)

Also according to Einstein equation, E = mc2.…………… 2)

Where m = mass of photon

From equation 1) and 2) we have

hѵ = mc2

m = hѵ/c2………….3)

m = h/c …………..4) {ѵ = c/}

From equation 3) and 4) we can calculate the mass of photons.

Dual nature of matter-de Broglie equation (wave nature of particle)

Louis de Broglie (1924) proposed that just as radiations have particle nature the

material particles are also associated with wave nature.

He also give a relation for calculating the wave length of the wave associated with

a particle of mass m moving with a velocity u is given below

 = h/mu

Derivation

The energy of photon of frequency v is given as

E = hѵ…………………….1)

According to Einstein

E = mc2…………………..2)

Where m = mass of photon

From eqn. 1) and eqn. 2) we get

mc2 = hѵ

m2 = hc/

Rearranging we get,

 = h/mc

This eqn. can be applied for material particle.

de Broglie pointed out that the same equation might be applied to material particle

by using m for the mass of the particle instead of the mass of photon and replacing

c the velocity of photon by v, the velocity of particle.

 = h/mv …………………3)

Equation 3) is called de Broglie equation and it may be written as

 = h/p ………………...4)

Where p is the momentum of the particle.

The wave associated with material particle or object in motion are called matter

waves or de Broglie waves.

Significance of de Broglie wave

The wave character put some restriction on how precisely we can express the

position of electron or any other small moving particle.

This is due to the reason that unlike particles waves not occupy a well-defined

position in the space and are delocalized. The wave nature of matter however has

no significance for objects of ordinary size because wavelength of the wave

associated with them is too small to be detected.

For example

A ball of mass 1.0 kg moving with a velocity of 1.0 m/s is associated with a wave

of  6.62x 10-34m which is too small to be detected.

 = h/mv

6.62 x 10-34 kgm2s-1/ 1.0 kg x 1.0 ms-1

= 6.62 x 10-34 m

= 6.62 x 10-22 pm
Therefore such bodies have predominantly particle character. Wave nature of

such bodies is insignificant.

On the other hand microscopic or sub microscope particles like electrons are

associated with matter waves of observe length.

For example

An electron moving with a velocity of 6.0 x 106 m/s is associated with a wave of

wavelength 1.21 x 10-10m (121 pm)

 = h/mv

6.62 x 10-34 kgm2s-1/ 9.1 x 10-31 kg x 6.0 x 106ms-1

= 1.21 x 10-10 m

= 121 pm

Thus it is quite evident that the de Broglie concept is more significant for

microscopic or submicroscopic particle whose wavelength can be measured.

Heisenberg’s uncertainty principle

The principle was proposed by Werner Heisenberg.

“It is impossible to measure simultaneously both the position and velocity (or

momentum) of microscopic particle with absolute accuracy or certainty”

Mathematically,

∆x x ∆p h/4𝜋

Where

∆x = uncertainty in position
∆p = uncertainty in momentum

h = plank constant

The sign means that the product of ∆x and ∆p can be either greater than or equal

to h/4𝜋. It can be never be less than h/4𝜋.

Since the minimum product of ∆x and ∆p is constant, it means that

∆x α 1/∆p

It follows therefore that if uncertainty in position (∆x) is less then uncertainty in

momentum (∆p) would be large. Similarly if uncertainty in momentum (∆p) is less

the uncertainty in position (∆x) would be large.

In order to observe the position of an object, light of some suitable wavelength is

made to fall on the object which scatters light.

Now when the scattered light enters our eyes we can see an object. For scattering

to take place the wavelength of the light used should be on the same order as the

size of the object.

If the object is of reasonable size its position and velocity will not be changed by

the impact of the light radiation. Thus it is possible to know both the position and

velocity of object exactly.

In case of microscopic particles like electron the impact of striking photon causes

large displacement from the normal path. As a result, both the velocity and the

momentum of the particle change and send the electron in the unpredictable

direction.

It may thus concluded that it is not possible to determine simultaneously both the

position and momentum of a small moving particles such as electron with absolute

accuracy, or in other words it implies that the position of electron cannot be known

exactly as postulated by Bohr’s. Instead it is only possible to predict the probable

region in a given space where we can find electron. Thus Heisenberg replaces the

concept of definite orbit by the concept of probability.

Quantum numbers

The sets of numbers which specific energy, size, shape and orientation of the

electron orbital are called as quantum numbers. These are principal quantum

numbers, azimuthal quantum numbers and magnetic quantum numbers.

In order to designate the electron, an additional quantum number called spin

quantum number is needed to specify spin of the electrons.

Thus each orbital in an atom is designated by a set of three quantum numbers

and each electron is designated by a set of four quantum numbers.

1. Principal quantum number (n)

It is the most important quantum number as it determines to a large extent

the energy of an electron. It also determines the average distance of an

electron from the nucleus.

It is denoted by n. It can have any whole number value such as 1, 2, 3, 4

etc. The energy levels corresponding to these numbers are designated as

K, L, M, N etc.

As the value of n increases, the electron gets further away from the nucleus

and its energy increases. The higher the value of n, the higher is the

electronic energy.

The energy of the electron in hydrogen atom is given by the relation En = -

22me4/n2h2

Where

m = mass of electron (9.1 x 10-31kg)

e = charge on the electron (1.6 x 10-19 C)

h = plank constant (6.63 x 10-34 Kgm2s-1 or J-s)

n = principle quantum number

For the first principal shell (K), n = 1 which means that this energy shell is of

lowest energy and lies closest to the nucleus.

For the second principal shell (L), n = 2 and for the third principal shell (M),

n = 3 and so on.
 The energy of the various principal shells increases as we move (outwards)

from the 1stlevel (K level)

Thus the energies of the various levels are in the order

K < L < M < N …………… and so on.

Or

1st< 2nd< 3rd< 4th …………… and so on.

According to the equation for En, the largest negative value of energy is

obtained when n has the smallest permitted value ie. when n = 1.The

maximum number of electrons in principal energy level is given as 2n2

2. The angular momentum quantum number or Azimuthal quantum

number (l)

This quantum number is related to the orbital angular momentum of electron.

This is denoted by l

In fact the orbital angular momentum of electron is given by the following

expression

h√l (l+1)
orbital angular momentum = 2π

The value of l gives the sub shell in which the electron is located. It also

determines the shape of the orbital in with the electron is located. The

number of sub shell within a principal shell is determined by the value of n

for that principal energy level.

 Thus l may have all possible values as whole number values from 0 to (n-1)

for each principle energy level.

Value of l = 0 1 2 3 4

Designation of sub shell = s p d f g

For n =1, I have only one value that is 0. It means that an electron in first

energy level can be present only in s sub shell (l = 0) so the1stenergy has

only one sub shell that is 1s

For n = 2, l can have values 0 and 1.It means that the electron in the second

principal energy level may be located either in s sub shell(l = 0) and p sub

shell(l = 1)

So the 2ndenergy level has only two sub shells i.e. 2s and 2p

For n = 3, possible values of l are 0 1 and 2.This implies that an electron in

the third principal energy level may be present either in s sub shell (l = 0) or

p (l = 1) or d (l =2)sub shell. So the 3rd energy levels have three sub shells

i.e. 3s, 3p and 3d.

It may be noted that in any main level, for a multi electron atom, the order of

energies of very sub shell is s < p < d < f

3. The magnetic quantum number (m)

This quantum number is denoted by m and refers to the different orientation

of electron cloud in a particular sub shell. These different orientations are

called orbital’s.
 The number of orbital’s in a particular sub shell with in a principal energy

level is given by the number of values allowed to m which in turn depends

upon the value of l. The possible values of m are all integral values from +l

through 0 to -l making a total of (2l+1)

For l = 0 (i.e. S sub shell) m can have only one value m = 0. It means that s

sub shell has only one orbital

For l = 1 (i.e. p sub shell) m can have three values +1, 0 and -1.

This implies that p sub shell has three orbital’s

For l = 2 (i.e. d sub shell) m can have five values +2, +1, 0, -1 and -2.It means

that d sub shell has five orbital’s.

For l = 3 (i.e. f sub shell)m care have seven values +3, +2, +1, 0, -1, -2 and

-3. Hence the f sub shell has seven orbital’s.

Energy Principle quantum Value Designation Value of No. of orbital’s

no. (n) of l of sub shell m
In a given sub In a given
shell (2l+1) energy level
(2n2)
K 1 0 1s 0 1 1
L 2 0 2s 0 1 4
1 2p +1,0,-1 3
M 3 0 3s 0 1 9
1 3p +1,0,-1 3
2 3d +2,+1,0,- 5
1,-2

4. Spin quantum number (s)

 This quantum number which is denoted by s does not follow from the wave

mechanical treatment but arises from the spectral evidences that an electron

in its motion about the nucleus also rotates or spins about its own axis.

The spin quantum number in fact describes the spin orientation of the

electron the electron. The electron spin can be either clockwise or

anticlockwise. The spin quantum number can have only two values which

are +1/2 and -1/2

The +1/2 value indicates clockwise spin (generally represent by an arrow

pointing upward direction) and -1/2 indicate anticlockwise spin (generally

represent by an arrow pointing downward direction). It may be noted that

value of spin quantum number are independent of the values of other three

quantum numbers.

Shapes of orbital’s

It has been observe that s orbital are independent of angular wave

function. but simply depend on radial part of a wave function. This means

that they do not have directional dependence. All s orbital are therefore

symmetrical, p and d orbital’s however depends upon radial as well as well

as angular wave function which means, that they show angular

dependence. The angular dependence of 1s, 2s and 2p orbital’s wave

function is shown in below figure.

Y
Y

+
 + X

1s 2s

The positive and negative sign in figure indicates that whether the orbital

wave function is positive or negative in a particular region. It may be noted

that one 1s orbital wave function has some sign everywhere. This is

equivalent to the wave produced by plucking the string between the two

points in the middle.

On the other hand, 2s orbital wave function can be positive or negative

depending upon the distance. In fact the sign of wave function changes

after the node. This is equivalent to wave produced when the string

between the two points is plucked at 1/4 of the distance.

s orbital’s

For s orbital the probability of finding the electron in all the direction is

same, at a particular distance. In other words, s-orbital’s are spherical

symmetrical. The picture of s orbital is shown in figure. The s-orbital of

higher energy level are also spherical symmetrical however, they are more

diffused and have spherical shells within them where probability of finding

the electron is zero. These are called spherical or radical nodes.

In 2s orbital there is one spherical node. In the ns orbital the number of

such spherical node is (n – 1).

The size of the s orbital increases with the increase in the value of the

principal quantum number (n).

Therefore, 4s > 3s> 2s > 1s.

p orbital’s

There are three possible orientation of electron cloud. These orientations of

orbital’s of a p sub shell are designated as px, py and pz orbital’s. px, py and pz
orbital’s are oriented along x axis, y axis and z axis respectively.

Each p orbital has two lobes which are separated by a plane of zero probability

called nodal plane.

Each p orbital is thus dumb-bell shaped.

d orbital’s

There are five possible orientation of electron cloud. these five orientations

or orbital’s are designated as dxy, dyz, dzx, dx2-y2 and dz2. Three of these

orbital’s dxy, dyz and dzx are identical in shape but different in

orientations. Each has four lobes of electron density bisecting the angles

between principal axis.

The dx2-y2 also has four lobes which lie along x and y axis. The dz2 has

two lobes lying along z axis and a ring of high electron density in the x y

plane.

Note that dz2 has a doughnut-shaped electron cloud in the center whereas

others have clover leaf shape.

Thus we may conclude that, Number of nodes in any orbital

= (n-l-1)

Where l = number of planar nodes in any orbital.

Pauli's exclusion principle

This principle was discovered by Wolfgang Pauli.

“No two electrons in an atom can have same values for all the four quantum

numbers”
All the electron in a particular orbital have same values of principal quantum

number (n), azimuthal quantum number (l) and magnetic quantum number (m)

For example

All the electrons in 3s orbital have n = 3, l = 0 and m = 0. Therefore in order to

have unique sets of quantum number they must have different value of spin

quantum number (s).

But we know s can have only two values +1/2 and -1/2. Hence, in an orbital only

two electrons can be accommodated, one spinning clockwise (s = +1/2) and other

spinning anticlockwise (s = -1/2).

From the above discussion we can derive the number of electrons in different

types of sub shells.

Types of sub shell No. of orbitals No. of electrons

s sub shell 1 1x2=2
p sub shell 3 3x2=6
d sub shell 5 5 x 2 = 10
f sub shell 7 7 x 2 = 14

Energy level diagram of multi electron atoms

1) The different sub shells of a particular energy level may have different

energies. For example, energy of 2s sub shell is different from the energy of

2p sub shell.

2) In a particular energy level, the sub level having higher value of l has higher

energy.
 For example energy of p sub shell (l = 1) is higher than energy of 2s sub

shell (l = 0).

In general, increasing order of energies of different types of sub shells in a

particular energy level is

s<p<d<f

3) As the value of n increases, some sub shells of lower energy levels may

have higher energy than the energy of some sub shells of higher energy

level.

For example energy of 3d is higher than the energy of 4s although the latter

belongs to the higher main energy level.

4) The increasing order of order of energies of various sub shell is

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p ……..

In a multi electron atom energy of electron is determined not only by principal

quantum number (n) but also by azimuthal quantum number (l). The relative

order of energies of various sub shells in a multi electron atom can be

predicted by the help of (n + l) rule or Bohr-Bury’s rule.

According to this rule

1) In neutral atoms of sub shell with a lower value of (n + l) has lower energy.

2) If two sub shells have equal value of (n + l), the sub shell with lower value

of n has lower energy.

Rules for filling of orbital’s in an atom

1) Aufbau principle

“The electrons are added progressively to the various orbital in the order of

increasing energies, starting with the orbital of the lowest energy.

Increasing order of various energy orbitals is

1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p , 6s < 4f < 5d < 6p <

7s ……….

2) Pauli's exclusion principle

This principle was discovered by Wolfgang Pauli.

“No two electrons in an atom can have same values for all the four quantum

numbers”

All the electron in a particular orbital have same values of principal quantum

number (n), azimuthal quantum number (l) and magnetic quantum number

(m)

For example
 All the electrons in 3s orbital have n = 3, l = 0 and m = 0. Therefore in order

to have unique sets of quantum number they must have different value of

spin quantum number (s).

But we know s can have only two values +1/2 and -1/2. Hence, in an orbital

only two electrons can be accommodated, one spinning clockwise (s = +1/2)

and other spinning anticlockwise (s = -1/2).

From the above discussion we can derive the number of electrons in

different types of sub shells.

Types of sub shell No. of orbital’s No. of electrons

s sub shell 1 1x2=2
p sub shell 3 3x2=6
d sub shell 5 5 x 2 = 10
f sub shell 7 7 x 2 = 14

3) Hunds rule of maximum multiplicity

“Pairing of electron in the orbital’s of a particular sub shell (p, d, f) does not

take place until all the orbital’s of the sub shells are single occupied; More

ever the singly occupied orbital’s must have the electron with parallel spin.

Electronic Configuration of elements

The distribution of electrons into different shells, sub shells and orbital’s
 of an atom is called its electronic configuration. Keeping in view the above

rules and representing an orbital by a box and an electron with its

direction of spin by an arrow, the electronic configuration of the atom of

any element can be represented. Alternatively the electronic

configuration of any orbital can be simply represented by the notation, nlx

Where n = number of the main or principal shell

l = symbol of the sub shell or orbital (s, p, d, f)

Thus, 4p1means that the p sub shell of the 4th main shell contains one electron.

To get the complete electronic configuration of an atom, a number of such

notations are written one after the other in the order of increasing energies of

the orbital’s starting always with the orbital’s of lowest energy, i.e. 1s (or in the

order of increasing energies of the principal shell with all the sub shells

grouped) together. Using the above two methods of representation, the

electronic configuration of the elements are discussed below.

Hydrogen (Z = 1), 1s1 Helium (Z = 2), 1s2

Lithium (Z = 3), 1s2 2s1

Beryllium (Z = 4), 1s2 2s2

Boron (Z = 5), 1s2 2s2 2p1

Carbon (Z = 6), 1s2 2s2 2p2

Nitrogen (Z = 7), 1s2 2s2 2p3

Oxygen (Z = 8), 1s2 2s2 2p4

Fluorine (Z = 9), 1s2 2s2 2p5

Neon (Z = 10), 1s2 2s2 2p6

Sodium (Z=11), 1s2 2s2 2p6 3s1

Magnesium (Z = 12), 1s2 2s2 2p6 3s2

Aluminum (Z = 13), 1s2 2s2 2p6 3s2 3p1

Silicon (Z = 14), 1s2 2s2 2p6 3s2 3p2

Phosphorous (Z = 15), 1s2 2s2 2p6 3s2 3p3

Sulphur (Z = 16), 1s2 2s2 2p6 3s2 3p4

Chlorine (Z = 17), 1s2 2s2 2p6 3s2 3p5

Argon (Z = 18), 1s2 2s2 2p6 3s2 3p6

Potassium (Z = 19), 1s2 2s2 2p6 3s2 3p6 4s1

Calcium (Z = 20), 1s2 2s2 2p6 3s2 3p6 4s2

Exceptional configuration of chromium and copper

Chromium and copper have five and ten electron in 3d orbital rather than

4 and 9 electron respectively as expected. The reason is that fully filled

orbital’s and exactly half filled orbitals have extra stability. The half filled

and completely filled degenerate orbitals provide extra stability to the

system due to,

1. Symmetrical arrangement

The electronic configuration in which all the orbital’s of same sub

shell are either completely filled or exactly half filled have relatively

more symmetrical distribution of electrons and therefore leads to

 more stability to the system.

For example: expected configuration of chromium is 3d4 4s2. But

shifting of one electron from 4s to 3d orbital’s make the

configuration more stable.

2. Stability due to exchange energy

The half filled and fully filled degenerate orbital’s have more

number of exchanges and consequently have large exchange

energy for stabilization.

The exchange means shifting of electrons from one orbital to

another within a same sub shell.

4
Let us compare the number of exchanges in 3d 4s2 and 3d54s1

configuration of chromium.

In 3d4 arrangements electronic exchanges are six which implies that there

are six possible arrangements with parallel spin in 3d4 configurations. In

3d5 arrangements electronic exchanges are ten. It is quite evident from

above discussion the total

number of exchanges in 3d5 arrangements is larger which leads to

relativity greater stability.

In the similar way it can be established that number of exchanges in 3d 10

configuration is larger than in 3d9 configuration, which makes 3d 10

configurations relatively most stable.

Writing the configuration in condensed form

It may be noted that configuration of atom can also be written in

condensed form by taking the configuration of noble gases as core. The

configuration of inert gases representing are written as

[He]2, [Ne]10, [Ar]18, [Kr]36, [Xe]54 and [Rn]56

For example: electronic configuration of Sc having atomic number may be

written as,

21Sc: [Ar]18 3d1 4s2

 Question Bank

1. Write down the electronic configuration of Cr, Mn, Fe, Co, Ni, Cu and Zn.

2. Explain isotopes, isobars, isotones and isoelectronics with suitable

examples.

3. Write the difference between orbit and orbital.

4. What is the value of Plank’s constant.

5. Write the difference between orbit and orbital.

6. Write down the main postulates of Bohr’s atomic model? Outline

the advantages and weaknesses of Bohr’s model of atom.

7. What is a Hydrogen spectrum? Explain how Bohr’s theory accounts

for the hydrogen spectra.

8. Explain how Bohr’s model of an atom explains the calculation of

energy of an electron in particular orbit of a hydrogen atom.

9. The ionization enthalpy of hydrogen atom is 1.312 x 106 Jmol-1.

Calculate the energy required to excite the electron in the atom

from n1 = 1 to n2 = 2.

10. Calculate the wavelength of the radiation emitted when an electron

in a hydrogen atom undergoes a transition from 4th energy level to

the 2nd energy level.

11. The energy associated with the first orbit in the hydrogen atom is –

2.18X10-18 J atom-1, what is the energy associated with the fourth

orbit.

12. Explain Quantum numbers and give significance of each quantum

 numbers.

13. What is the maximum number of unpaired electrons in a p-sub shell?

a) Designate the orbital’s in terms of s, p, d, f having following

quantum numbers:

i) n = 4, l = 3 ii) n = 3, l = 1 iii) n = 3, l = 0 iv) n = 3, l = 1

14. An electron is in a 4f orbital. What possible values for the quantum

numbers, n, l, m and s can it have?

15. Designate the orbital’s in terms of s, p, d, f having

following quantum numbers:

i) n = 4, l = 3 ii) n = 2, l = 0

16. Write short notes on the following: i)Hunds rule ii)Aufbau

principle iii) Pauli’s exclusion principle

17. State de Broglie equation. How would the wavelength of a moving

object vary with mass?

18. State Heisenberg’s uncertainty principle. Give its mathematical

expression.

19. Draw and discuss the shapes of d-orbital’s.

20. Explain why atoms with half filled and completely filled orbitals

have extra stability?

 MCQ

1. The nucleus of the atom (Z>1) consists of

a) Proton and neutron

b) Proton and electron

c) Neutron and electron

d) Proton, neutron and electron

2. Bohr’s model can explain

a) Spectrum of hydrogen atom only

b) Spectrum of any atom or ion having one electron only

c) Spectrum of hydrogen molecule

d) Solar spectrum

3. Maximum number of electrons present in “N” shell is

a) 18

b) 32

c) 2

d) 8

4. Which statement is correct for an electron that has n = 4 and m = -2?

a) The electron may be in a d orbital

b) The electron is in the nth orbit

c) The electron may be in a p orbital

d) The electron must have a spin quantum number +1/2

5. The maximum number of electrons possible in a sub-level is equal to

a) 2l+1
 b) 2n2

c) 2l2

d) 4l+2

6. Transition from n = 4, 5, 6 to n = 3 in the hydrogen spectrum gives

a) Laymen series

b) Paschen series

c) Balmer series

d) Pfund series

7. The maximum number of unpaired electrons present in 4f energy level is

a) 5

b) 7

c) 10

d) 6

8. Non directional orbital is

a) 3s

b) 4f

c) 4d

d) 4p

9. The n+l value for the 3p energy level is

a) 4

b) 7

c) 3

d) 1
10. Which principle/rule limits the maximum number of electrons in an

orbital to two?

a) Aufbau principle

b) Pauli’s exclusion principle

c) Hund’s rule of maximum multiciplicity

d) Heisenberg’s uncertainty principle.