Chapter 12

Atoms
Thomson Model of Atom- (plum pudding model)
The first model of atom was proposed by J. J. Thomson in 1898.
▪ According to this model, the positive charge of the atom is uniformly
distributed throughout the volume of the atom .
▪ The negatively charged electrons are embedded in it like seeds in a
watermelon.
This model is also called plum pudding model of the atom.

Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom

Ernst Rutherford , a former research student of J. J. Thomson, proposed a
classic experiment of scattering of these α-particles by atoms to investigate
the atomic structure. The explanation of the results led to the birth of
Rutherford’s planetary model of atom (also called the nuclear model of the
atom).

Alpha-Particle Scattering
At the suggestion of Ernst Rutherford, in 1911, H. Geiger and E. Marsden
performed scattering experiment.

Alpha-particles emitted by a 214 83𝐵𝑖 radioactive source were collimated into a

narrow beam by passing through lead bricks. The beam was allowed to fall
on a thin foil of gold of thickness 2.1 × 10–7 m. The scattered alpha-particles
were observed through a rotatable detector consisting of zinc sulphide
screen and a microscope.
Observations
▪ Many of the α-particles pass through the foil. It means that
they do not suffer any collisions.
▪ Only 0.14% of the incident α-particles scatter by more than 1º.
▪ About 1 in 8000 of incident α-particles deflect by more than 90º.

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Rutherford argued that , greater part of the mass of the atom and its positive
charge were concentrated tightly at its centre. When the incoming α-particle
make a close encounter with the positive charge ,that would result in a large
deflection.
Rutherford’s nuclear model of the atom
▪ Most of an atom is empty space.
▪ The entire positive charge and most of the mass of the atom
are concentrated in the nucleus with the electrons some
distance away.
▪ The electrons would be moving in orbits about the nucleus just
as the planets do around the sun.
▪ The size of the nucleus to be about 10–15 m to 10–14 m.
▪ The electrostatic force of attraction, between the
revolving electrons and the nucleus provides the
centripetal force to keep them in their orbits.
Impact Parameter (b)

Impact parameter is the perpendicular distance of the initial velocity vector

of the 𝛂 𝐩𝐚𝐫𝐭𝐢𝐜𝐥𝐞 from the centre of the nucleus.
Alpha-particle trajectory
The trajectory traced by an α-particle depends on the impact parameter, b of
collision.

▪ For an α-particle close to the nucleus , impact parameter is

small and it suffers large scattering.
▪ For head on collision, the impact parameter b=0 and
α particle rebounds back ie,angle of scattering 𝜃 =1800.
▪ For large impact parameter, the angle of scattering will be
small ( 𝜃 ≈00) and such α particles go undeviated.

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Electron orbits
The electrostatic force of attraction(Fe), between the revolving electrons and
the nucleus provides the centripetal force (Fc) to keep them in their orbits.
Fc = Fe
mv2 1 e2
=
r 4πε0 r2

The kinetic energy (K) of electron

𝟏 𝟐 𝐞𝟐
K = 𝒎𝒗 =
𝟐 𝟖𝛑𝛆𝟎 𝐫
The potential energy (U) of electron
−𝐞𝟐
U=
𝟒𝛑𝛆𝟎 𝐫
(The negative sign in U signifies that the electrostatic force is in the –r
direction.)
Thus the total energy E of the electron in a hydrogen atom is
E = K+U
e2 e2
E= −
8πε0 r 4πε0 r
−𝐞𝟐
E = 𝟖𝛑𝛆
𝟎𝐫

The total energy of the electron is negative. This implies the fact that the
electron is bound to the nucleus. If E were positive, an electron will not
follow a closed orbit around the nucleus.
Limitations of Rutherford Model
Rutherford nuclear model has two main difficulties in explaining the
structure of atom:
(a) Rutherford model could not explain stability of
matter. The accelerated electrons revolving around the
nucleus loses energy and must spiral into the nucleus.
This contradicts the stability of matter.
(b) It cannot explain the characteristic line spectra of atoms of
different elements.

Atomic Spectra
Each element has a characteristic spectrum of radiation, which it emits.
There are two types of spectra-Emission spectrum and Absorption
spectrum.

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Emission Spectrum
When an atomic gas or vapour is excited at low pressure, by passing an
electric current through it, the emitted radiation has a spectrum which
contains certain specific wavelengths only. A spectrum of this kind is termed
as emission line spectrum and it consists of bright lines on a dark
background. Study of emission line spectra of a material is used for
identification of the gas.

Absorption Spectrum
When white light passes through a gas and we analyse the transmitted light
using a spectrometer we find some dark lines in the spectrum. These dark
lines correspond precisely to those wavelengths which were found in the
emission line spectrum of the gas. This is called the absorption spectrum of
the material of the gas.

Expression for Radius of Hydrogen Atom

Consider an electron of charge ‘e’ and mass ‘m’ revolving round the
positively charged nucleus in circular orbit of radius ’r’
𝐧𝟐 𝐡𝟐 𝛆𝟎
𝐫𝐧 = -----------(3)
𝛑𝐦𝐞𝟐
th
rn is the radius of n orbit of Hydrogen atom
𝐫𝐧 𝛂 𝐧𝟐
For the first orbit n=1
h2 ε0
r1 =
πme2

This is called the Bohr radius, represented by the symbol a0

𝐡𝟐 𝛆𝟎
𝐚𝟎 =
𝛑𝐦𝐞𝟐

Bohr radius , 𝐚𝟎 = 5.29 × 𝟏𝟎−𝟏𝟏 m = 0.53Å

The radius of 𝐧𝐭𝐡 orbit of Hydrogen atom can also be written as

𝐫𝐧 =0.53 𝐧𝟐 Å

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 𝐫𝟏 =1 x 0.53 Å
𝐫𝟐 =4 x 0.53 Å
𝐫𝟑 =9 x 0.53 Å

The Line Spectra of The Hydrogen Atom

De Broglie’s Explanation of Bohr’s second postulate of Quantisation

De Broglie argued that electron in its circular orbit behaves as a particle
wave. The particle wave can produce standing wave under resonant
condition.

For 𝒏𝒕𝒉 orbit of radius 𝑟𝑛 , the resonant condition is

2 π 𝑟𝑛 = n λ----------- (1) where n=1,2,3…..

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But by de Broglie hypothesis , for matter waves
𝐡
λ = ---------------(2)
𝐦𝐯

Substituing eqn (2) in eqn (1),

𝐡
2 π rn = n
𝐦𝐯
𝐧𝐡
mv 𝐫𝐧 = where n=1,2,3……
𝟐𝛑
This Bohr’s second postulate of Quantisation.

Limitations of Bohr Atom Model

(i) The Bohr model is applicable to hydrogenic atoms. It cannot be
extended two or more electron atoms. Difficulty lies in the fact that
each electron interacts not only with the positively charged nucleus
but also with all other electrons.
(ii) While the Bohr’s model correctly predicts the frequencies of the
light emitted by hydrogenic atoms, the model is unable to explain
the intensity variations of the frequencies in the spectrum.

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