CBSE Class 12 Physics 2014 Outside Delhi Set 1 Paper

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Question : 9
Total: 30
Using Rutherford model of the atom, derive the expression for the total energy of the electron in hydrogen atom. What is the significance of total negative energy possessed by the electron?
OR
Using Bohr's postulates of the atomic model, derive the expression for radius of n‌th ‌ electron orbit. Hence, obtain the expression for Bohr's radius.
Solution:  
According to Rutherford,
‌
mv2
r
‌
=‌
1
4πε0
‌
Ze2
r2

mv2‌=‌
1
4πε0
‌
Ze2
r

‌ Total energy ‌‌=‌ P.E. ‌+‌ K.E. ‌
‌=−‌
1
4πε0
‌
Ze2
r
+‌
1
8πε0
‌
Ze2
r

‌=−‌
1
8πε0
‌
Ze2
r

The negative sign shows that electron-nucleus form an abound system.
OR
According to Bohr's model, electrons revolve around the orbits such that their angular momentum is an integral multiple of ‌
h
2Ï€

mvr‌=‌
nh
2Ï€

‌
mv2
r
‌
=‌
1
4πε0
‌
Ze2
r2

r‌=‌
ε0n2h2
Ï€Ze2m
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