A Seminar onDIFFERENT ATOMIC MODELS

Presented by:SHANTI SHARMA4TH SEMESTER

Thomson’s Atomic Model Drawbacks of Thomson’s Atomic

Model Bohr atom model Drawbacks of Bohr atom model Sommerfeld’s atom model Sommerfeld’s relativistic atomic model Drawbacks of Sommerfeld’s atom model The vector atom model Conclusion References

CONTENTS

Thomson’s Atomic Model

J. J. Thomson

1. Electron enter into the constitution of all atoms2. Since the atom as a whole is electrically neutral the

quantity of positive and negative charge in it must be the same.

Drawbacks

He explained that hydrogen can give rise only to a single spectral lines.He couldn't explain the fine spectra

BOHR ATOM MODEL

Niels Bohr

He proposed the following postulates-

(1)An electron cannot revolve round the nucleus in all possible orbit. It can revolve round the nucleus in those allowed orbits for which the angular momentum of the electron is an integral multiple of .

2h

Bohr’s atomic model

(2)An atom radiates energy only when electron jumps from a stationary orbit of higher energy to one of lower energy. If electron jumps from an initial orbit of energy to the final orbit of energy ,a photon of

frequency is emitted.

iE)( fif EEE

h

EE fi

The Bohr formulae

r-e

Radius of the nth permissible orbit for hydrogen

me

hnrn 2

022

The total energy of the electron in the nth orbit

2220

24

8 hn

ZmeEn

+Ze

Different spectral series of hydrogen atom according to Bohr.

Lyman

Balmer

Paschen

Brackett

Pfund

n=1

n=2

n=3n=4

n=5

n=6n=7

The energy level diagramThe equation Can be diagrammatically

represented. Then it is called The energy level diagram. ----------------------------------------------------

2220

24

8 hn

ZmeEn

n=1

n=2

n=3

n=4n=5

n=6n

Lyman

BalmerPaschen

Brackett

Pfund

-13-6

-3.4

-1.5

-085

)(eVEn

H H H

DrawbacksSpectrograph of high resolving showed that lines are not single. Each spectral lines actually consisted of several very close line packed together. This is called fine structure of spectral lines. Bohr theory could not explain this fine structure. Sommerfeld’s atom modelSommerfeld introduced two main modification in Bohr’s model: (1)The path of an electron around the nucleus, in general ,is an ellipse with the nucleus at one of the foci.

(2)The velocity of the electron moving in an elliptical orbit varies considerably at different parts of the orbit.

N

electron

r

Elliptical orbit for hydrogen atom

The condition that determines the allowed elliptical orbit is

When and the orbit become circular

has n different values

0,, abnn

n

n

a

b

0nnn

n

1,1 nn

2,2 nn

1,2 nn

3,3 nn2,3 nn

1,3 nn

2220

24

8 hn

ZmeEn

TOTAL ENERGY

Sommerfeld’s relativistic atomic model

The velocity of electron in the elliptic orbits is C137

1

So Sommerfeld taking into account the variation of mass with velocity.

He showed that the relativistic equation describing the path of the electron is

)1(

cos112

ar

2220

2

422

161

cp

ez

(1)

4220

244

2220

24 1)4

3(

88 nn

n

h

Zme

hn

ZmeEn

is called the fine structure constant

The path of the electron given by equation(1) is an ellipse whose major axis precesses slowly in the plane of the ellipse about an axis through the nucleus.

The total energy in the relativistic theory

137

1

2 0

2

ch

e

Line is due to the transition from n=3 state to n=2 state of hydrogen atom.

Fine structure of the lines

H

H

12

22

132333

Drawbacks

Sommerfeld’s theory was able to give an explanation of the fine structure of the spectral line of hydrogen atom. But he could not predict the correct of spectral lines.

The vector atom modelThe two distinct features of vector atom model are:

The conception of spatial quantizationThe spinning electron hypothesis

Quantum no. associated with the Vector Atom Model

• A total quantum number n, it can take only integral values 1,2,3..etc

• An orbital quantum number l, which may take any integral value between 0 and (n-1) inclusively.

• A spin quantum number s, the magnitude of which is always ½.

• A total angular quantum number j, the resultant angular momentum of the electron due to both orbital and spin motions i.e vector sum of l and s.

Vector atom Model for Orbital Angular Momentum

The orbital angular momentum for an atomic electron can be visualized in terms of a vector model where the angular momentum vector is seen as precessing about a direction in space.

The diagram shows that the possible values for the "magnetic quantum number" ml for l=2 can take the values ml =-2,-1,0,1,2or, in general, ml=-l,-l+1,……..,l-1,l

Vector atom Model for Total Angular Momentum

When orbital angular momentum L and electron spin angular momentum S are combined to produce the total angular momentum of an atomic electron, the combination process can be visualized in terms of a vector model.

Conclusion

Vector atom model can explain Zeeman effect, Stark effect.

It can also explain the complex spectra of alkali metal like sodium.

And also can explain how the orbital electrons in an atom are distributed

around the nucleus.

• ATOMIC PHYSICS - J.B. RAJAM

• INTRODUCTION TO ATOMIC SPECTRA -HARVEY ELLIOTT WHITE

• http://www.tutornext.com/lesson/vector-atom-model/1243900

• http://www.chembio.uoguelph.ca/preuss/1_5_VectorModel.pdf

References

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