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Test Index
JEE Main Physics Class 12 Atoms and Nuclei Part 1 Questions
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© examsnet.com
Question : 74
Total: 100
Suppose an electron is attracted towards the origin by a force
k
r
where
′
k
' is a constant and '
r
' is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the
n
th
orbital of the electron is found to be '
r
n
' and the kinetic energy of the electron to be
′
T
′
n
. Then which of the following is true?
[2008]
T
n
∝
1
n
2
,
r
n
∝
n
2
T
n
independent of
n
,
r
n
∝
n
T
n
∝
1
n
,
r
n
∝
n
T
n
∝
1
n
3
,
r
n
∝
n
2
Validate
Solution:
Given,
Centripetal force
=
k
r
Then
k
r
=
m
v
2
r
⇒
k
=
m
v
2
⇒
T
n
=
1
2
m
v
2
=
1
2
k
Tn is independent of n
Also,
Angular momentum,
L
=
n
h
2
π
⇒
m
v
r
n
=
n
h
2
π
(
∵
L
=
m
v
r
)
⇒
r
n
=
n
h
2
π
√
k
m
(
∵
m
2
v
2
=
k
m
or
m
v
=
√
k
m
Clearly,
r
n
∝
n
© examsnet.com
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