Bohr Vector Model
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Transcript of Bohr Vector Model
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
hEE fi
The Bohr formulae
r‐e
Radius of the nth permissible orbit for hydrogen
mehnrn 2
022
The total energy of the electron in the nth orbit
2220
24
8 hnZmeEn
+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 hnZmeEn
n=1
n=2
n=3
n=4n=5
n=6n
Lyman
BalmerPaschen
Brackett
Pfund
‐13‐6
‐3.4
‐1.5
‐085
)(eVEn
HH 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
nn
ab
0nnn
n
1,1 nn
2,2 nn
1,2 nn
3,3 nn2,3 nn
1,3 nn
2220
24
8 hnZmeEn
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. 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(cos11
2
ar
2220
2
422
161
cpez
(1)
4220
244
2220
24 1)43(
88 nnn
hZme
hnZmeEn
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
1371
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
HH
12
22
13 2333
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 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 Sare 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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