HISTORICAL ASPECTS OF ATOM MODEL

•What is the structure of atom?• How the electrons are arranged in the atom?

The question was first replied by J.J. Thomson by suggesting an atom model.

THE QUESTION IS

It states that all the matter are composed of a very small particle called atom which is indivisible.

“THIS THEORY FAILS”As he was unable to distinguish the different types

of particles.

JOHN DALTON THEORY(1803):

• Electrons are embedded within spherically distributed, positive charge (so-called “plums in the pudding” model)

• Both the positive charge and the mass of the atom would be more or less uniformly distributed over its size.

THOMSON ATOM MODEL(1898):

• The negative charges came from within the atom.• A particle smaller than an atom had to exist.•The atom was divisible!

SO,• Thomson called the negatively charged “corpuscles,” today known as electrons.

• Since the gas was known to be neutral, having no charge, he reasoned that there must be positively charged particles in the atom.

CONCLUSIONS OF THOMSON ATOM MODEL

Problems of Thomson Model

• He could never find the positive charge particle.• He was unable to explain the radiation emitted by an

atom? But this model soon came into conflict with experiments by Rutherford.

The Rutherford ExperimentsRutherford discovered α (alpha)-particles;

α-particles are the nuclei of helium atoms, which were produced by nuclear disintegration.

He used α-particles in various studies.In 1909, he with co-workers (Hans Geiger and Ernest

Marsden) experimented with streams of alpha particles passing through a thin gold foil.

The foil thickness was ~8.6 x 10-6 cmThe foil was so thin that it had to be supported on a glass

plateThe plate without any foil was transparent to the alpha particles.

Rutherford Experiment

A TRANSMITTED BEAMS (LITTLE OR NO DEFLECTION )B SCATTERED BEAM (SMALL DEFLECTION)C SCATTERED BEAM ( LARGE DEFLECTION)

OVSERVATIONS :As most of the alpha particles pass through the gold foil, without any deflection, most of the space within the atom is empty.As some of the alpha particles were deflected by large angles, they must have approached to some positive charge region called as nucleus.As very few of the alpha particles experience the deflection, it was concluded that the volume occupied by the nucleus is very small.Since alpha particles, which are comparatively denser, were deflected by the nucleus, it shows that almost the complete mass of the atom must be within the nucleus.

The nucleus is very small - positively charged - with the electrons outside the nucleus.

A new question arises. If the electron is negatively charged, won't the attraction for electrons by the nucleus cause the electron to fall into the nucleus and therefore atoms should collapse.

RUTHERFORD'S MODEL OF THE ATOM

Rutherford explained his experimental results.

By considering the solar system - the planets are attracted by the sun under universal gravitation. Yet planets are not pulled into the sun. As they are in motion around the sun and this motion prevents them from being pulled into the sun.

And according to Earnshaw's theorem , a system of charge particle cannot remain at rest in stable equilibrium under the influence of purely electrostatic force.

SO RUTHERFORD PUTS THE ELECTRON IN MOTION AROUND THE NUCLEUS.

ATOMIC SPECTRAWhen an atomic gas or vapour at low pressure is excited usually by passing

electric current through it, the gas/vapour emits radiations of certain specific wavelength only. A spectral of this kind is called line emission spectrum and it consists of a few bright lines on a dark background.

When white light is pass through the same gas/vapour, we observed a bright background crossed by few dark lines signifying missing wavelength or wavelength that are absorbed by gas . They form the line absorption spectrum.

HYDROGEN SPECTRUM

The spectrum of hydrogen atom consists of a numbers of lines which fall into the region of definite sets which are called series. The line in each series are such that their separation and intensity decrease regularly toward shorter wavelength converging to a limit called the series limit.

The first such spectral series are reported by J.J.Balmer in1885 and is called the Balmer series of Hydrogen.

And is to be discuss later in detail.

LIMITATION OF RUTHERFORD ATOM MODEL

As electron is in accelerating motion, it must radiate energyin the form of electromagnetic wave.So, electron spiral inward and eventually fall into the nucleus .

According to classical electromagnetic theory the frequency of the emitted electro

magnetic wave must be equal to the frequency of the revolution of the electron .

As the revolving electron spiral inward , the frequency of the emitted electromagnetic wave must change continuously . Therefore , atom should emit continuous spectrum . This is not so in actual

THUS, CLASSICALLY RUTHERFORD ATOM IS . NOT STABLE .

SO THIS MODEL IS DISCARDED

BOHR THEORY OF ATOM MODEL

• Neils Bohr(1885-1962), a Danish physicist, purposed an atom model in 1913. • In order to eliminate the short coming of Rutherford atom model.He made following three postulates

BOHR’s 1st POSTULATE

• Postulate of stationary orbit In an atom , the electron

are moving in a stationary circular orbit around the nucleus such that the centripetal force is provided by electrostatic force of attraction between electron and nucleus.

BOHR’S 2ND POSTULATEPostulates of quantization of angular momentum (quantum postulate)

The orbit of electron which are allowed are those for which the angular momentum of an orbiting electron is an integral multiples of ℏ

BOHR’S 3RD POSTULATE

Postulate of radiation

An electron orbiting in a stationary circular orbit doesn’t radiate energy at all even though classical electromagnetic theory predicts that accelerated charge particle emit electromagnetic radiation . Radiation is emitted only when an electron in an initial higher orbit having energy Ei

Jumps to a final orbit of energy Ef (Ei >Ef) . An emitted photon will have the frequency

STATIONARY ORBIT DUE TO de BROGLIE

According to de Broglie , a stationary orbit is the one whose perimeter must be an integral multiple of de Broglie wavelength.

Thus, de Broglie statement is in agreement with Bohr’s postulate.

From Bohr’s 1st postulate

From Bohr’s 2nd postulate

APPLICATION OF BOHR’s THEORY

By solving this two eqns , we get

For hydrogen the radius of 1st orbit

This is known as Bohr radius

And the value of orbiting velocity

For hydrogen in the 1st orbit

This is known as “FINE STRUCTURE CONSTANT”.

Energy of the orbiting electron

From 1st postulate

And

For Hydrogen atom

For ground state energy of hydrogen, n=1

Hence the ground state energy of hydrogen is -13.6eV

Energy level diagram

This eqn can be represented diagramatically and is called

energy level diagram

When n=1, E1 =-13.6eVWhen n=2, E1 =-3.4eVWhen n=3, E1 =-1.51eVWhen n=4, E1 =-0.85eV

EXPLAINATION OF LINE SPECTRA Emission of radiation occur only when an electron jumps from one higher energy level to another lower energy level. The frequency of this emitted radiation is given by

Thus , the radiation is emitted as a single photon of light . Hence Bohr’s model successfully explain the existence of line spectra.

BOHR’S INTERPRETATION OF HYDROGEN SPECTRUM

The frequency of the emitted radiation

,

=Rydberg’s constant

7 6 5 4 3 2 n=1

BALMER SERIES

LYM

AN S

ERIE

S

PFUND SERIES

PASCHEN SERIES

BRAC

KETT

SERI

ES

ELECTRON TRANSITION DIAGRAM

0-0.37-0.54-0.85

-1.51

-3.4

-13.6

n=6n=5n=4

n=3

n=2

n=1

Lyman series

Balmer series

Paschen series

Brackett series

Pfund series

ENER

GY

IN (e

v)

ENERGY LEVEL DIAGRAM SHOWING SPECTRAL SERIES

FORMULA FOR RADIATION FOR SPECTRAL LINE FOR HYDROGEN

1) Lyman series

For lyman series limit, n=∞

For the first line of Lyman series: n=2

For the second line of Lymanseries: n=3

2)BALMER SERIES

This formula was already predicted by J.J. Balmer in 1885

For 1st line for balmer series, n=3

This line is known as line of hydrogen

For second line of balmer series, n=4

This line is known as line of hydrogen

For 3rd line for Balmer series, n=5

This line is known as line of hydrogen

For 4th line for Balmer series, n=6

This line is known as line of hydrogen

For Balmer series limit , n=

3)Paschen series

4)Bracket series

5) Pfund

WAVE LENGTH LIMIT SPECTRAL LINESPECTRAL SERIES

LOWERSTATE

UPPERSTATE

LOWERSTATE

UPPER STATE

1)LYMANSERIES

1 2 1216 1 912

2)BALMERSERIES

2 3 6563 2 3696

3)PASCHENSERIES

3 4 18751 3 8220

4)BRACKETTSERIES

4 5 40515 4 14585

5)PFUNDSERIES

5 6 74584 5 22789

*************

∞

∞

∞ ∞

∞

912 1216 3646 6563 8220 18751

LYMAN BALMER PASCHEN

ABSORPTION SPECTRA OF HYDROGEN

In the absorption spectrum of hydrogen, absorption line only in lyman series appear. Normally, the atom is always in the ground state i.e, n=1 therefore , absorption transition can occur only from n=1 to n>1.Hence, lines of only lyman series appear on the screen.

INCLUSION OF NUCLEAR MOTION

In 1914, Bohr suggested that both the nucleus and its orbital electron revolves around a common centre of mass with same angular velocity as nucleus has finite mass M.Thus, we should consider the reduced mass of electron of mass m and the nuclear mass M

. Therefore , the mass m in the earlier expression of energy is to be replaced by the reduced mass µ.

In this consideration of reduced mass, Bohr’s postulate becomes

and

Similarly,

and

Therefore, the wave number is given by

,

Rydberg constant for hydrogen atomIf we replace the electronic mass m by the reduced mass µ in the earlier expression for Rydberg constant , we will get a reduced value of Rydberg constant.

,with

And,

i.e,

RYDBERG CONST IS VARIED FOR DIFFERENT NUCLEI

For hydrogen atom, the Rydberg constant is

for singly ionized helium atom, Rydberg constant is

For doubly ionised lithium atom,

,

,

EVIDENCE IN THE FAVOUR OF BOHR THEORY

The ratio of mass of electron to the mass of proton

This value is in excellent agreement with the value obtained by the other method.

,with

DISCOVERY OF DEUTERIUMDeuterium was first predicted by Berge and Menzel in 1931. But it was discovered by Harold Urey and his co-worker in 1932

,

The wavelength of the emitted radiation when electron undergoes transition from n=3 to n=2 of deuterium has a shorter wavelength 6561Å that of the line of wavelength 6563Å.But the intensity is less.

EXCITATION AND IONIZATION POTENTIAL

The minimum energy required to raise an atom from one energy level to another is called an excitation energy. So, when this energy is expressed in electron volt(eV) it is term as EXCITATION POTENTIAL.

The energy required to removed an electron completely free from the influence of the nucleus of the atom is calledIonization energy. So, when this energy is expressed in electron volt, it is term as IONIZATION POTENTIAL.

BOHR MODEL AS SEMI CLASSICAL MODEL

Bohr’s theory is a combination of some ideas of classical physics and quantum physics.• Bohr used the classical electrostatic coulomb force of attraction and ideas of centripetal force are used. • Bohr used the quantum theory of quantization of angular momentum.•Bohr applied the quantum condition of Max Planck.

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