Atomic Structure

Nature of Electromagnetic Radiation & Atomic Spectra

Nature of Light

1. Corpuscular Theory- This theory was proposed by Newton. According to this theory, light is
composed of tiny particles known as corpuscles. This theory explained the phenomena of
reflection & refraction but failed to explain the phenomena of interference & diffraction.

2. Wave Theory- Maxwell found that an alternating current of high frequency radiated in the
form of waves which travelled in space w/ the same speed as that of light. These waves were
called Electromagnetic Waves or EMR as they were associated with both electric & magnetic
fields.
It assumes that EMR propagate in the form of continuous waves.
Features-

a. Light is transmitted in the form of Electromagnetic Waves.

b. Electromagnetic waves are associated w/ electric & magnetic waves directed at right
angles to each other & also perpendicular to direction of propagation of the wave.

c. All the electromagnetic waves travel with same speed which is equal to speed of light.

d. These waves don’t require a medium for their propagation/transmission.

e. Ex- X-rays, UV Rays. IR radiations, etc.

3. Wave motion & Its characteristics- Wave is a periodic disturbance in space. Wave motion
represents the propagation of this periodic disturbance which carries energy.

a. Amplitude- The height of a crest or the depth of a trough from the line of propagation of
wave. Amplitude determines the intensity of the radiation.
Point of maximum amplitude is called crest. The point corresponding to the minimum
value of the amplitude on the negative side is called the trough.

b. Wavelength ( λ)- The distance between the two consecutive crests or troughs.
1 Å= 10−8 cm = 10−10 m

c. Frequency ( ν )- The no. of waves passing through a reference point in one second.

d. Velocity ( c )- The distance travelled by a wave in one second is velocity.

c = ν x λ
All types of EMR travel with same velocity.

Atomic Structure 1
 e. Wave Number ( ν )- The no. of waves which can be accommodated in a unit length.
ν = λ1 
​

4. Electromagnetic Spectrum- It is the

arrangement of different types of
electromagnetic radiations in the
increasing order of wavelength or
decreasing order of their frequency.

5. Planck’s Quantum Theory of Radiation-

a. Radiant energy is emitted or absorbed discontinuously in the form of small energy

bundles or energy packets known as quanta or photons.
This implies that radiations obtained from excited atoms consist of a stream of photons &
not continuous waves.

b. Each quantum of radiation is associated with a definite amount of energy depending

upon the frequency of radiation.

⁍=⁍=⁍

c. A body can emit or absorb energy only in an integral/whole number multiple of quantum.
Thus, radiant energy can be emitted as hv, 2hv, etc.

6. Black Body Radiation-

Black body is an object that is able to absorb all the radiations falling on it and emits
electromagnetic radiations which has continuous frequency distribution when kept at a
uniform temperature.
The radiations emitted by a black body is called black body radiation.

a. This phenomenon cannot be explained by corpuscles & wave theory. Only Planck's
quantum theory can explain it.

b. A black body at room temp. appears black because the energy emitted by it corresponds
to frequencies in infra-red region & cannot be perceived by human eyes.
When temp. is increased it appears dull red. On increasing more, it become yellow, white
& finally blue-white.

7. Photoelectric Effect (Albert Einstein)- When a beam of light of sufficiently high energy is
made to fall on the surface of a metal, electrons are ejected. This phenomenon is known as
photoelectric effect. The electrons ejected are called photoelectrons.

a. This incident light should have a certain minimum frequency to eject electrons from a
particular metal. This frequency is known as threshold frequency.

b. Kinetic energy of the ejected electrons increases linearly with the frequency of the
incident light & does not depend upon the intensity of the incident light.

c. No. of photoelectrons ejected increases with increase in intensity of incident light.

Atomic Structure 2
 T otal − Energy = W ork − F unction(ϕ) + K.E.

K.E. = h(ν − ν) − − − − − − − − − − − −ϕ = hν

8. Dual Nature of Light-

a. The explanation of photoelectric effect as suggested by Einstein recommends that light is

composed of photons. A photon may be regarded as a particle of light. Hence, the
explanation of photoelectric effect is in accordance to the corpuscular theory of light
which assumes that light is composed of stream of particles.

b. The phenomenons (diffraction, interference, polarization of light, etc.) can be explained

only the the wave theory of light.

c. Therefore, light has a dual nature—> Particle and Wave nature.

Atomic Spectra

1. Spectrum- A plot of intensities of the constituent parts of radiation emitted or absorbed by a

substance against their wavelengths, frequencies, wave numbers in increasing/decreasing
order.
It is a continuous spectrum due to the collective behaviour of a large no. of interacting atoms.
The separation of light into constituent wavelengths in a definite sequence by a prism or a
grating is called dispersion.

2. Atomic Spectra- It is the spectrum obtained on account of the characteristic behavior of an

individual atom. It consists of sharp well defined lines corresponding to definite frequencies.

a. Emission Spectra- When the radiations emitted by atomic species are analysed by a
prism or grating, the spectra obtained contain distinct bright lines. This type of spectra is
called emission spectra.

i. Also called line spectra due to the presence of distinct lines.

ii. The molecular species also give emission spectra but their spectra contain groups of
lines called bands.

iii. Line spectrum can be obtained by heating the vapour of an element at low pressure,
by passing electric current or by passing a discharge through an elemental gas at low
pressure & analyzing the emitted radiation by a prism or a grating.

iv. Atomic spectra of an element differs from the spectrum of some other element.
Rubidium and caesium were discovered by study of atomic spectra.

b. Absorption Spectra- It is the spectrum obtained by the selective absorption of certain

wavelengths by a substance from the electromagnetic radiations to which it is exposed.
Atomic absorption spectra is the spectrum consisting of dark lines. When EMR are
passed through a substance containing atomic species, the atoms present in it may
absorb certain characteristic wavelengths. Dark lines are observed in place of those
wavelengths which are absorbed by the substance.

c. Emission Spectrum of Hydrogen Atom

ν = λ1 = RZ 2 ( n12 − n12 )
​ ​ ​

Atomic Structure 3
 Bohr’s Model for Hydrogen & Hydrogen like atoms

Postulates

1. The electrons move around the nucleus in certain specifically permitted circular orbits known
as energy shells. An electron is associated with a definite amount of energy.

2. While moving in a particular energy level or energy state, an electron neither losses nor gains
energy. The energy of an electron in a particular energy state remain fixed/stationary.
The energy states are also called stationary energy states as the energy of an electron in an
energy state is fixed or stationary.

3. Only those energy levels/energy states are permitted in which the angular momentum of an
electron is an integral multiple of h/2

4. On absorption of energy from an external source, an electron may jump from a lower energy
level to a higher energy level. In coming back from a higher level to a lower energy level,
electron emits energy.
Energy gained or lost in these transitions is always quantized & is equal to the difference of
the energies of the two levels involved in the transition.

Jumping of electron from one energy level to another is called transition.

Excitation is the transition from a lower energy level to a higher energy level.
Deexcitation is the transition of electron from a higher energy level to lower energy level.

Quantisation of Energy- Quantisation refers to be in well defined specific amounts.

When a quantity is said to be quantized, it means that the given quantity neither varies
continuously nor can have arbitrary values. It can have only well defined values.

Atomic Structure 4
 Merits of Bohr’s model- It successfully explained the atomic spectra of H & H like atoms & also
provided a reasonable explanation to the stability of an atom.

1. Stability of Atom- An electron neither gains or losses energy whole moving in a particular
shell. This implies that if an atom is not disturbed, its constituent electrons will go on moving
in their specified orbits for ever & atom will remain stable.

2. Energy of electron in a particular Orbit- Bohr’s postulates enable us to derive an expression

for the calculation of the energy of an electron in a particular orbit.

Negative value of Energy- Energy of electron in nth shell has a negative value. This is
because of the fact that the energy of an electron in the infinite shell is regarded as equal to
zero.
When electrons are at an infinite distance from nucleus, they do not experience any nuclear
attraction.

3. Explanation of Atomic Spectrum of Hydrogen- According to Bohr when a electron

deexcites, it emits energy. The energy thus emitted is quantized & corresponds to a definite
frequency or wavelength. This forms the basis of existence of a large no. of well defined
lines in the atomic spectrum of hydrogen.

a. Ground state is the energy state corresponding to the minimum energy. Hydrogen atom
consists of 1 electron in K shell which is ground state.

b. When H atom is provided energy from an external source, the electron present in ground
state gets excited and jumps to state of higher energy. This state is known as excited

Atomic Structure 5
 state.

c. Excited state is very short lived for abt 10−8 seconds. Therefore, the excited electron can
not stay for a longer time in the excited state. It is forced to drop to a lower energy level.

4. Defects of Bohr Model

a. Model is unable to explain the spectra of atoms containing more than one electron.

b. This model is unable to explain the fine spectrum of atoms. The fine spectrum of an atom
contains many more closely spaced lines than predicted by Bohr’s model.

c. It is unable to explain the effect of electric & magnetic fields on the spectra of atoms.
Zeeman Effect- Splitting of spectral lines when magnetic field is applied on an atom.
Stark effect- Splitting of spectral lines when electric field is applied on an atom.

d. Heisenberg’s Uncertainty Principal states that the position & velocity of an electron can
never be determined simultaneously & accurately. This gave a setback to this model.

e. It cannot explain the mode of formation & geometry of molecules which are formed by
the union of two or more atoms. This model does not provide any explanation how the
atoms would combine together to form molecules.

Wave/Quantum Mechanical model of Atom

1. Dual nature of Electron (De Broglie’s Equation)

a. The properties of moving electrons indicate that they have a dual nature. An electron
behaves both as a particle & wave.

b. It has mass & possess K.E. Hence, it should be a particle. But it can also be diffracted like
light waves, hence, it should be a wave. This dual behaviour problem of electron posed a
big problem which was solved by de Broglie.

c. He suggested that all moving material objects show dual nature. Every particle which
possess mass & velocity behaves as both wave and particle.

h h
λ= =
2mKE
​ ​

mc ​

Wavelength is inversely proportional to its mass.

2. Heisenberg's Uncertainty Principle- It is not possible to determine simultaneously the

position & momentum of a moving microscopic particles with absolute accuracy.
Dual nature of electron posed restrictions on the simultaneous & accurate determination of
its conjugate properties such as position & velocity or momentum.

h h
ΔX ∗ ΔP > − − − or − −ΔX ∗ ΔP >
4π 4πm
​ ​

Wave Mechanical Model

Schrodinger Wave Equation- The quantum mechanical model of an atom is a very important
equation known as Schrodinger wave equation. It describes the behaviour of electron waves in
atoms & molecules⇒

Atomic Structure 6
 Significance of wave function ( ψ )-

1. It represents the amplitude of the electron wave. The square of wave function (ψ 2 ) gives the
probability of finding the electron at various places in a given region around the nucleus.

2. The probability of finding an electron in different regions is different as varies from place to
place.

3. This equation is a second order differential equation. It has several solutions. Some are
imaginary & not acceptable.
Schrodinger wave equation is solved for given atom which gives several values of wave
function.

4. Acceptable wave should be finite, single valued, continuous & should be zero at infinite
distance.

5. Acceptable values of wave function are called eigen-functions. Characteristic values of E

called eigen values are used to solve the equation.
Orbitals are those regions where the wave functions provide the probability of finding an
electron to be maximum.

Orbit Orbital

It is a 3-D region in space around the nucleus in

It is a well defined circular path in which electrons which the probability of finding an electron is
were supposed to move in Bohr model. maximum in accordance to Quantum mechanical
model.

Orbits are non-directional. Except ‘s’ orbit, all other orbitals are directional.

Orbit can accommodate a max. of 2n^2 electrons. It can accommodate a max of 2 electrons only.

Revolution of an electron in an orbit is against

It is in accordance to the principal.
Heisenberg’s Uncertainty principal.

Probability distribution of charge cloud in different

Orbits are circular. orbitals is different. This gives them different
shapes.

Filling of Electrons in Different Orbitals & Electronic Configuration of Elements

Rules for filling of electrons

1. Pauli Extension Principle- An electron in atom can be defined completely by a set of four
quantum numbers n, l, m & s. This is possible only when the set of four quantum numbers for
an electron is unique/different.

a. This principle controls the assignment of the values of four quantum no. to an electron.
Two electron in an atom can never have identical sets of four quantum numbers.

b. The set of 4 quantum numbers of an electron in an atom is unique, a particular shell in an

atom can accommodate as many electrons as are the possible sets of 4 quantum no. for
it.

c.

Atomic Structure 7
 i. Maximum no. of electrons that can be accommodated in a shell is 2n2 , where n is
PQN.

ii. ‘s’ subshell can accommodate a max of 2,

‘p’ subshell a max of 6,
‘d’ subshell a maximum of 10
‘f’ subshell a max of 14 e− .

2. Hund’s Rule of Maximum Multiplicity- It helps in filling the orbitals of an atom.

While filling different orbitals of a subshell, the electrons prefer to remain unpaired as far as
possible & possess the same direction of spin.
Pairing of electrons takes place only when all the orbitals of a subshell are singly occupied.
Pairing taxes place in an opposite direction as in the same direction they will have identical
values of n, l & m.

3. Aufbau Principle- It helps in explaining the building up of an atom by the filling of electrons
in its various orbitals.
In the ground state of an atom, the electrons enter into the available orbitals in the increasing
order of energies & fill up the orbitals of lower energy first.

Atomic Structure 8
 4. Energy Level Diagram

Atomic Structure 9