Introduction

As we have already studied about Daltons Atomic Theory of Matter, and later it was
concluded that Atom is made up of 3 sub -atomic particles. The particles are Electron, Proton
and Neutron. In this chapter ,we will study about different attempts made to explain atomic
models .The phenomenon that leads to development of dual nature of Light and Matter .Also,
we will deal with the methods to be followed while writing electronic configurations, and
much more . Let us see that first how these fundamental particles were discovered, and how
they are arranged in structure of Atom.

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DISCOVERY OF ELECTRON:

The Electron was discovered by J.J Thomson by conducting a Cathode ray tube experiment.

For the experiment he used Crooke’s tube, which was 60cm long glass tube and had a small
tube attached. To this small tube vacuum pump was attached, it also had two metal plates
which were connected to battery by wires.

The tube contained gas at atmospheric pressure. when current at high voltage (10,000volts)
was passed following observations were made:

1. When current was passed through a gas at 1 atmospheric pressure and at a very high
voltage, nothing happened. That is no visible effect was seen inside the tube.
2. Then further the pressure of gas was reduced by pumping the air out, with the help of
vacuum pump. The pressure was reduced to 10-2atm, then on passing current it was seen
that whole tube started glowing green.
3. Then further the pressure was reduced to 10-4It was seen the whole glow vanished, but it
was seen that at the end of the tube (anode side) there was a faint green glow observed.

To confirm the faint glow anode was made perforated, and a zinc sulphide screen (fluorescent
material) was placed behind it.

When current was passed under same conditions it also started glowing green. This
confirmed that under those conditions some rays were emitted through cathode, and were
travelling towards anode. Those rays were called as cathode rays and found to consist of
negatively charged particles called electron.
Properties of cathode rays

1. They are found to travel in straight line. This property was concluded by performing an
activity where the object was placed in their path. When they strike it ,they casted the
shadow of the object as shown below:

2. Cathode rays are formed of material particles. This property was concluded by
performing an activity where in their path a paddle was mounted on an axle.When they
strike it ,they rotated the paddle .

3. They are negatively charged.This property was concluded by performing an activity

where electric and magnetic field was applied, they deflected towards positive plate and
in presence of magnetic field they deflected towards north pole.

4. When they strike some metal surface, they heated it. So, it was concluded they can also
produce heating effect.
 5. They cause ionization of gas through which they passed.
6. They produce x-rays when strike against the hard metal like tungsten etc.
7. They can make florescent material glow, when strikes some fluorescent material.
8. They affect the photographic plate.
9. They have penetrating effect.

From the above properties and experiment it was concluded that cathode rays are made up
of negatively charged particles called electron.

Further experiments were carried out in order to know the charge and mass of electron. It was
found to be:

 Charge :1.6 x 10-19C

 Mass 9.1 x 10-31kg

We can define electron as:

 “A fundamental particle that is negatively charge of magnitude 1.6 x 10-19C and

mass equal to 9.1 x 10-31

DISCOVERY OF PROTON:

IT WAS DONE BY E. GOLDSTEIN

 In 1836 the same experiment was carried out where the same conditions
were provided. The gas at low pressure was taken and current was passed.

 The high voltage between the electrodes was passed. It was found that when
cathode rays passed through the gas, they ionized the gas by taking electrons
along, leaving behind positively ionized gas particles.

 These particles were travelling towards cathode.These particles were found to

form the beam of rays of positively charged particles and were called as canal
rays.

 These rays consist of positively charged particles called a proton.

Properties of anode rays

1. They also travel in straight line.

2. They are also made up of particles.
3. They carry positive charge.
 4. Their ratio of charge to mass was different for different gas that was taken in
tube.
5. The mass of particles were found to be different for different gases. It was
nearly equal to the mass of atom.

When hydrogen gas was taken in the tube its mass was found to be minimum. As we
know, Hydrogen atom is the lightest one and its charge to be same as Electron. It is
1.6x10-19C and its e/m ratio taken as standard that is 1.67x 10-24g.

Proton is defined as a

“fundamental particle which carries one-unit positive charge and mass nearly
same as hydrogen atom.”

DISCOVERY OF NEUTRON:

It was discovered by Chadwick. In which he bombarded some light elements with

fast moving alpha particles. He found, that some new particles were emitted which
carried no charge and had mass equal to that of proton.These neutral particles were
named as neutron.

So, neutron is defined as:

“the fundamental particle which carries no charge and mass equal to that of
hydrogen atom.”

ATOMIC MODELS OF ATOM

J.J THOMSON PLUM PUDDING MODEL

In 1904, the attempt to explain structure of Atom was done by J.J Thomson.

According to Thomson :Atom is positively charged sphere in which few negative

charges are scattered at certain places like plums in pudding or cherries in ice
creams.
Limitation of this model: However, this model failed. The reason about failure was
as it wasn’t possible that few negative charges remain scattered in the positive
sphere. As we know, opposite charges attract each other. So, these negative
charges would have been neutralized. They can’t remain scattered. However, this
couldn’t be explained by Thomson therefore the model failed.

RUTHERFORD SCATTERING EXPERIMENT:

In order to explain the structure of atom, Rutherford performed the scattering

experiment.

For this, he took Gold foil and passed Alpha rays through it. The source of these
Alpha rays was radioactive substance which was kept in a Lead block (as Lead is
inert towards it). These rays were made to pass through a slit. Alpha rays are
actually positively charged rays consisting of Helium nucleus (He). To notice the
scattering of rays, he fitted movable screen made of florescent material around the
gold foil.
Following observations were made: -

1. Some rays passed straight.

2. Some rays were deflected through small & large angles.
3. Some rays rebound back.

Conclusion drawn:

 Most of the space in atom is empty.

 There is something in center of an atom called Nucleus.
 Nucleus is +vely charged.

So, According To Rutherford ,structure of an atom is similar to solar system.

He said,

 Atom is electrically neutral.

 Nucleus is in center.
 In which protons & neutrons are present.
  Outside nucleus electrons revolve like planets revolve around sun.

He said, atom is made of two parts: nucleus and extra nuclear part .

In Nucleus, positive charge is present and in extra nuclear part electrons are present
as shown in figure:

Proton -> (+)vely charged

Electron -> (-)vely charged

Neutron -> No charge

Limitation : he failed to explain the stability of an atom”.

According To Electromagnetic theory, a charged particle revolving in circular

path continuously emits energy and shorten its path.

As we know, Electrons are also a charged particle revolving in circular path. So, they
should also emit energy and shorten its path .As a result, they should finally fall into
nucleus. But this doesn’t happen.

Some definitions were also given related to atom:

Atomic number: It is equal to number of protons in an atom .It is represented by

‘Z’and is written as subscript.

Atomic Mass: It is equal to number of nucleons, or we can say sum of protons and
neutrons in nucleus of an atom. It is represented as ‘A’ and is written as superscript.

Representation of atom of an element

It is the method of representation of element by specifying its symbol, atomic number

and mass number .The rule involved is writing symbol and specifying its atomic
number as subscript and mass number as superscript.
ISOTOPES, ISOBARS, ISOELECTRONICAND ISOTONES:

 ISOTOPES: Are those elements which have same atomic number ,but
different mass number.


 ISOBARS: Are those elements which have same mass number, but different
atomic number.


 ISOTONES: Are those elements which have same number of neutrons.
 Example:- C6N7O8 ( all have 8 electrons)
 ISOELECTRONIC: the species containing same number of electrons.
 Example:- O7-, F-, Mg2+,Al3+ (all have 10 electrons)

Numericals:-

Question 1: Calculate the number of protons, neutrons and electrons in 80/35

Bromine?

Answer 1:-

Question 2: Find out the atomic numbers, mass number and number of protons?
Answer 2:-

DUAL NATURE OF LIGHT: DEVELOPMENT LEADING TO BOHR’S MODEL

There were so many factors, phenomenon that lead to the failure of Rutherford
model:

1. Dual nature of matter

2. Atomic spectra

But before studying Bohr model, we need to learn electromagnetic radiations.

Newton said the corpuscles of light possess wave nature of light.

It was able to explain reflection, refraction etc. But failed to explain phenomenon of
interface or diffraction. So, particle nature of light was considered.

Let us study about dual nature. It is electromagnetic theory, which was given by
Huygens.This proved wave like character of

Light and tells us about wave motion. Wave motion is like if you throw stones, you
will see a ripple that is wave.

Electromagnetic theory: According to this theory

1. Energy is emitted or absorbed continuously in the form of radiant energy.

2. These radiations consist of electric and magnetic field acting perpendicular to
the direction of propagation of wave.
3. These waves can travel through medium as well as through vacuum.
4. The radiations travel with speed =3x108m/sec.

Characteristics of wave
  Wavelength: It IS Distance between two crest or trough.

Units Used:- pm(picometer)

1 pm:- 10-12

1nm :- 10-9

1nm :- 10-10

 Frequency: number of waves produced in one second.

 Units Used:- sec-1, Hertz
 Velocity of light: It is distance travelled with respect to time in any direction.
 Units Used:- m/sec
 Amplitude: maximum displacement of particle from its mean position.
 Units Used:- m or cm
 Wave number: number of waves in 1cm length.

Electromagnetic spectrum

When all the electromagnetic radiations are arranged in order of increasing

wavelengths, and decreasing frequencies the complete spectrum is called
electromagnetic spectrum as shown below:

Limitations of this theory

It failed to explain various phenomenons that are mentioned below:

1. Black body radiations.

2. Photoelectric effect.
3. The variation of heat capacity of solids at different temperatures.
4. The line spectra of atoms.
Black body radiation and Photoelectric effect

Particle nature of Electromagnetic radiations :There were two important

phenomenon that couldn’t be explained by considering Light with wave character:

The phenomenon is:

 Black body radiation

 Photoelectric effect

Lets first study about the nature of these phenomenon:

1. Black body radiation: Black body is defined as perfect emitter and absorber
of light.

For example, whenever we heat an Iron ball like objects, on heating they become
first Red, then Orange, then Yellow and at very high temperature they become
White.

According to the electromagnetic theory, the energy is emitted or absorbed

continuously. So, the radiations emitted may vary in intensity, but should have same
colour. The change in color shows, that wavelength also changes .This indicates non
continuous flow of energy. So, it couldn’t be explained by electromagnetic theory.
This phenomenon shows, that if we keep on heating the light that it emits. It will
show changes in wavelength. That means the wavelength keeps on decreasing but
after White there is no further change.

2. Photoelectric effect

It is the ejection of electrons from metal surface when light of suitable wavelength
strikes the metal surface.

The apparatus set to demonstrate this effect is given below:

To check the current flow, the ammeter is introduced in the circuit. The following
observations were noticed:

1. Light of suitable frequency can only eject electrons. Every metal surface has a
set value of frequency that can cause ejection and that corresponding
frequency is called threshold frequency (vo).
2. Number of electrons ejected is directly proportional to intensity of light.
3. Kinetic energy of electron is directly proportional to frequency of light that
strikes the surface.
4. The graphs drawn below shows the above observations:

So, these two-phenomenon Black body and Photoelectric effect couldn’t explain,
considering light as a wave. To explain these two phenomena a new concept and
new theory was put forward. According to which, light was supposed to possess a
particle like character.

Problem 1:

1. Calculate (a) wave number and (b) frequency of yellow radiation having wave
length of 5800 A?

Answer –

1. Calculation of wave number: wave number = 1/wave length

 1. Calculation of frequency: frequency = velocity(C) /wave length

2. The Vivid Bharti station of all India Radio, Delhi broadcasts at a frequency of
1368 KHz (kilohertz). Calculate the wave of the Electromagnetic radiation
emitted by the transmitter. Which part of the Electromagnetic spectrum does it
belongs to ?

Answer : wave length = speed of light / velocity

Planck’s quantum theory:

According to this theory:

1. Energy emitted or absorbed is not continuous, but is in the form of packets

called quanta .In terms of light it is called as photon.
2. Each photon carries an energy which is directly proportional to the frequency
of wavelength i.e. E depends upon v (nu).
1. Or E=hv (where v is frequency)
2. Value of h =6.634 x 10-34Jsec
3. Energy associated with no of packets is given by:

E=nhv (where n is an integral multiple)

This formula can also be written as:

E = (nhc)/ (λ)

(Because we know frequency=speed of light/wavelength)

V = (c/ λ)
EXPLANATION OF BLACK BODY AND PHOTOELECTRIC EFFECT ON THE
BASIS OF QUANTUM THEORY.

For the ejection, minimum frequency is required called threshold frequency .Let’s say
light that falls, has energy equal to hv .Out of this h , a amount of h is used as
binding energy and rest is given to electron as kinetic energy.

Following observations were made

1. If frequency is greater than threshold frequency: Than ejection occurs and

also, kinetic energy is imparted to ejected electron.
2. If frequency is equal to threshold frequency, than only ejection occurs.
3. If frequency is less than threshold frequency, than no ejection occurs and no
kinetic energy is imparted.

Please note hvo is called as wave function.

Black body radiation

When light falls on the surface, the particles gain energy and starts oscillating. When
more energy is supplied the oscillations increase, amplitude increase .Therefore, the
colours keep on changing.

Problem 1:

1. Calculate the energy of a mole of photons of radiation whose frequency is 5 x

1014 Hz?

Answer 1:-

1. A 100-watt bulb emits monochromatic light of wave length 400 nm. Calculate
the number of photons emitted per second by the bulb.

Answer 1:-
EMISSION AND ABSORBTION SPECTRA

Atomic spectra: Absorption and Emission spectra.

This is the phenomenon that gave serious blow to Rutherford model.It can be
defined as: ‘splitting of light’ into various colours or colour bands is called spectra.”

When we see VIBGYOR the Violet colour merges into another and likewise other
color merges into another.

So, in that case:

 Where one-colour merges into another and there is no definite boundaries,

that spectra is called continuous spectra.
 If we study it for atoms the spectra obtained is discontinuous spectra.
 The study of spectra is called spectroscopy

Atomic spectra are of two types

 Emission spectra
 Absorbtion spectra

Emission spectra: It is obtained when emitted light is analyzed.The light is emitted

when an atom is heated or electric current is passed.These are also referred as
finger prints of atoms.

The apparatus is set as shown in figure:

When we analyze with spectrometer the spectra obtained is discontinuous. When
white light is passed through the sample it absorbs few radiations and then
transmitted light is analyzed.

Emission spectra of hydrogen

 The hydrogen gas ,at low pressure is taken in the tube.

 Then light emitted by it was examined
 It was noticed that spectra obtained consist of large number of closely spaced
lines which falls in different regions as shown:

Rydberg gave the formula to determine the wavelength of these lines. That is:

Limiting line: the limiting line in H spectrum was when n2=infinity

Problem:

Question 1: Calculate the wave length of the spectral line obtained in the spectrum of
Li2+ ion when the transition takes place between two levels whose sum is 4 and the
difference is 2?

Answer 1:-

According to Bohr:

 Atom is electrically neutral i.e., number of Protons = number of

Electrons.
 In centre of an atom, a dense body or heavy mass called Nucleus is
present. In which Protons and Neutrons are present.

 Protons are positively charged

 Neutrons are Negatively charged

 Outside Nucleus, shells or energy levels designated as K, L, M, N ----so on

are present.
 The electron in the atom moves around the nucleus in a fixed circular
path called orbits. These orbits are associated with definite energy, and
that can be expressed as

Energy

The energy of shell is given by –

E = -13.6

Energy calculation for same atom in different energy level.

Energy calculation for different atom in different energy level.

Radius –

The radii of stationary states are given by

rn = a0n2 also called bohr radii.

Radii calculation for same atom

Radii calculation for different atom

Velocity

The velocity of electron in different orbits are given by:

Vn = 2.18 x 106 m/s

Velocity calculation for same atom –

Velocity calculation for different atom –

 The energy of electron is quantized.

 Only those orbits are permitted in which angular momentum of electron
is integral multiple of h/2π.
  The electron in its ground state neither absorb or emit energy that is it
keeps on revolving in orbit without losing any energy.
 Energy is emitted or absorbed only when electron jumps from its lower
state to higher state called as excited state.

 The excited state being unstable, electron returns to its ground state and
in doing so it emit the absorbed energy equal to:

E = E 2 - E1
Success of Bohr’s model:

1. It explained stability of an atom.

2. It explained the spectrum of hydrogen:
EXPLANATION OF HYDROGEN SPECTRA

According to Bohr,

 When energy is supplied to atoms of hydrogen, the electron from

lower energy gets excited to higher energy level.
 The excited state being unstable, it jumps back to its original state
that is ground state.
 Some electrons move to their ground state in one jump, some in
multiple jumps. Each jump corresponds to line in a spectrum.
 As we know the gas in tube consists of many hydrogen atoms.
 Therefore, each electron on getting energy gets excited.
 On returning to the ground state, they either move in single jump or
multiple jump.
 This is the reason that we get so many lines in different regions in
hydrogen spectrum.

The wavelength emitted by them can be calculated as:

Limitations of Bohr model of an atom:

1. Bohr model failed to explain the line spectra of multi-electron

atoms.
2. He couldn’t explain splitting of line in the magnetic field (Zeeman
effect) and in electric field (stark effect).
3. He failed to explain three-dimensional model of an atom.
4. He was unable to explain the shapes of molecule.
5. He couldn’t explain the dual nature of matter and Heisenberg
uncertainty principle.

This led to the discovery of Quantum mechanics. Let us first understand

the dual nature of matter and Heisenberg uncertainty principle that
couldn’t be explained by Bohr model.

DUAL NATURE OF PARTICLE: DEBROGLIE AND HEISENBERG

UNCERTAINTY PRINCIPLE
As we have studied that light has dual character .That is particle as well
as wave character. In the same way, it was proved that all material
particles too have wave like character.

It was explained by De-Broglie: According to him when any particle is in

motion it emits wave.”

The wavelength associated with it is given by:

Significance of De- Broglie relation

In real life, it does not have any significance. This is because in real life we
come across only macroscopic objects which have significant mass. So,
the wavelength emitted by them is almost nil. The wavelength is
significant only for microscopic bodies, but in real life we do not come
across microscopic objects.

Derivation of Bohr postulate of angular momentum from de

Broglie relation

According to Bohr model, the electron move around the nucleus in circular
orbit. According to De Broglie, the wave can be in phase or can be out of
phase. For the wave to be in phase the circumference should be integral
multiple of wavelength that is:

Hence it also derives the postulate of bohr’s model.

Problem : Calculate the mass of a photon with wavelength 3.6A

Heisenberg uncertainty principle

According to Heisenberg ,it is impossible to measure both the position and momentum of
moving particle with accuracy.

 If value of position is small ,it can be measured accurately but not momentum.
 If value of momentum is small it is measured accurately but not the position.

Mathematically that means:

Explanation:

 Suppose we need to measure position accurately, than we need to use light.

 So, that the photon of light must strike the electron and reflected photon is seen with
microscope.
 Due to hitting, the position and velocity of electron is changed.
  But to pin point position, the light of shorter wavelength should be used.
 The shorter wavelength means high frequency and high energy.
 So, this high energy photon may change the speed and direction of particle.

Significance

This holds good only for microscopic particles, as energy of photon is not enough to change
the position and velocity of bigger bodies. So, in our daily routine it has no significance.

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QUANTUM MECHANICS

It was given by Schrodinger. He said if we take both the characters in account that is particle
character and wave character, we have to define a property that is a wave function.

Schrodinger wave equation

On the basis of it Schrodinger simplified equation as:

Physical significance of wavefunction: ”

  It gives the amplitude associated with it. But if we do square of it, than it gives the
probability of finding the electron in particular region.

Orbital: It is three-dimensional space, where probability of finding an electron in maximum.

Difference between orbit and orbital:

Orbital: They are of four types

 s orbital: Spherical in shape, non-directional. It has only 1 orbital therefore, can

accommodate only 2 electrons.
 P-orbital: dumb-bell shaped and directional. It has 3 orbital (px, py, pz). It can
accommodate maximum of 6 electrons.
  d-orbital: It has double dumbbell, directional. It has 5 orbital (dxy,dyz,dzx,dx2-y2,dz2).It can
accommodate maximum of 10 electrons
 F-orbital: It has diffused shape. It has 7 orbital therefore, can accommodate maximum of
14 electrons.

Quantum numbers

They are set of 4 numbers, which give complete information about the address of electron.

There are 4 types of quantum numbers:

 Principal quantum number.

 Azimuthal quantum number.
 Magnetic quantum number.
 Spin quantum number.

Principal quantum number:

 It is represented as ‘n’.
 It was given by Bohr.
 It represents the orbit where electron is going to be present.

Uses:

1. It gives number of electron in orbit by formula 2 n2.

2. It gives angular momentum of electron.
3. It gives energy of electron.
4. It gives radius of orbit.

1. Azimuthal quantum number:

 It gives information about sub shell of an atom.

o It is represented as ‘l’.
o It was introduced by Somerfield.
o It always has value (n-1).

Example: if n=1 ,l=0

If n=2,l=0,1

If n=3,l=0,1,2

1. Magnetic quantum number:

 It describes the behavior of electron in magnetic field.

  It is represented as ‘m’.
 It was given by land.
 Its value is equal to –l,0, +l

For example: if n=1, l=0, m=0 that is only one orbital

If n=2, l=0,1, m=-1,0, +1 that is three orbitals

1. Spin quantum number:

o It gives the info about spinning of electron about its axis i.e. clockwise or
anticlockwise
o It is denoted by ‘s’.
o Its value is either =+1/2, -1/2

Problem: Write down the quantum numbers n , l and m for the

Following orbitals:

1. 3d x2 – y2
2. 4d z2

Answer :-

n=3, l=2, m=+2

N = 4, l=2, m=0

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Pauli’s exclusion Principle

According to it: “no two electrons can have the same set of all four
quantum numbers.”

Or, it states that an orbital can have maximum of two electrons and that
must be of opposite spin. Due to this, it was concluded that an orbital can
have maximum of two electrons which can have all 3-quantum number
same but the spin will be definitely different.

Shapes of atomic orbitals:

1. s –orbital

Its shape is spherical.For 1s the probability of finding electron is maximum

near nucleus and it decreases as we move away from nucleus.
For 2s: Again, probability of finding electron is maximum near nucleus and
decrease as the distance increase. But it has one ring in it, where
probability of finding electron is zero that is a nodal plane or a node.

The shape of 2s differs from 1s as it has one node and 1s has no node.
Similarly, in 3s there are two nodes.

The different s orbitals differ from each other in number of nodes, size and
energy.

2. Shape of p orbital

Its shape is dumb-bell. It is found that probability of finding electron is

maximum in both the lobes. There is a plane passing through nucleus
where probability of finding the electron is almost zero. That is nodal
plane.

There are 3 sub-shells: px, py and pz.

It is directional in nature.All the 3 p orbitals are degenerate that is have

same energy.

3. Shape of d orbital:

It has 5 subshells:dxy,dyz,dzx,dx2-y2 and dz2

There shapes are given as shown:

The shape of dz2 is called as doughnut shape or baby soother type shape.

Number of nodes in any orbital can be calculated by: (n-l-1).

RULES OF WRITING ELECTRONIC CONFIGURATION:

“It is the number of electrons in different orbitals. “

There are certain set of rules that are followed:

Aufbau principle: It states that in ground state of atom, the orbitals are
filled in order of their increasing energies. That is electrons first occupy
the lower energy orbital then higher energy orbitals are filled.

The orbitals are filled in order:

1s,2s,2p,3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,6p,7s,5f,6d,7p…

To know the energy of orbital with lower energy the n+l rule is
followed:

According to it:

1. The lower the value of n+l for an orbital, the lower is its energy and
is filled first.

For example: Out of 2s and 2p ,2s is filled first as n+l for 2s, is 2+0=2 and
for 2p it is 2+1=3. Therefore, 2s is filled first.

1. If two orbitals have same value of n+l , than the orbital with lower
value of n is filled first.

For example: Out of 3p and 4s, n+l for both is 4 . Therefore, 3p is filled
first as it possess lesser value of n.

1. Pauli’s exclusion principle: According to it, an orbital can

accommodate maximum of two electros and that must be of
opposite spin.

For example: If orbital has s2, then the orbital has the arrangement as
given below.

Correct incorrect

2. Hund’s rule of maximum multiplicity: According to it, electron

pairing in degenerate orbital will not take place until and unless,
each orbital is singly filled.

For example,if the d orbital has d6 ,then the filling is not:

  Sodium (Na)

Atomic number=11

Electronic configuration = 1s2,2s2,2p6,3s1

 For Potassium(k) :Atomic number =19

Electronic configuration = 1s2,2s2,2p6,3s2,3p6,4s1

For Aluminum ion

Atomic number of Aluminum =13

Aluminum ion (Al3+)=1s2,2s2,2p6

EXCEPTIONAL ELECTRONIC CONFIGURATION OF CHROMIUM AND

COPPER
For Copper (Cu)= [Ar]18,4s23d9

But actually, it has : [Ar]18,4s13d10

Similarly, for Chromium it should be: [Ar]18,4s23d4

But in actual it is:=[Ar]18,4s13d5

The reason behind is:

1. Half-filled and fully filled orbital are more stable

If configuration is 4s2 3d9 , then the d orbital is not fully filled. If

configuration is 4s1 3d10 , then the d orbital is completely filled. That means
it becomes more stable.

2. The more is the exchange energy more stable is the orbital as

shown below:

If configuration was 4s23d4 the exchange energy is:

Total number of exchanges = 3 + 2 + 1 = 6

If configuration is 4s13d5the exchange energy is:

Total number of exchanges = 4 + 3 + 2 + 1 = 10

So, more is the exchange energy -more is the stability.