The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom if [a0 is Bohr radius]
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Answered by
1
Answer:
The nuclear attraction on the electron = Centrifugal force
So,
r
2
kZe
2
=
r
mv
2
v
2
=
mr
kZe
2
...(i)
Angular momentum, mvr=n
2π
h
v
2
=
4π
2
m
2
r
2
n
2
h
2
...(ii)
Comparing (i) and (ii)
mr
kZe
2
=
4π
2
m
2
r
2
n
2
h
2
r=
Z
n
2
[
4π
2
mke
2
h
2
]=
Z
n
2
a
0
∴ v
n
=
2πa
0
n
hZ
KE=
2
1
mv
n
2
=
8π
2
ma
0
2
n
2
h
2
Z
2
KE(for n=2,Z=1)=
32π
2
ma
0
2
h
2
.
Hence, the correct option is C
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