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Test Index
JEE Main Physics Class 11 Kinetic Theory of Gases Part 1 Questions
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© examsnet.com
Question : 24
Total: 100
The potential energy (U) of a diatomic molecule is a function dependent on
r
(interatomic distance) as
U
=
α
r
10
−
β
r
5
−
3
where,
α
and
β
are positive constants. The equilibrium distance between two atoms will be
(
2
α
β
)
a
b
, where
a
=
.
.
.
.
.
.
.
.
.
[25 Feb 2021 Shift 1]
Your Answer:
Validate
Solution:
Given, potential energy,
U
=
α
r
10
−
β
r
5
−
3
As we know for equilibrium, differentiation of potential energy with respect to distance
(
d
u
d
r
)
=
0
⇒
d
d
r
(
α
r
10
−
β
r
5
−
3
)
=
0
⇒
d
d
r
(
α
r
−
10
−
β
r
−
5
−
3
)
=
0
−
10
α
r
−
11
+
5
β
r
−
6
−
0
=
0
⇒
10
α
r
−
11
=
5
β
r
−
6
⇒
2
α
r
−
11
=
β
r
−
6
⇒
2
α
β
=
r
−
6
r
−
11
=
r
5
⇒
r
=
(
2
α
β
)
1
∕
5
⇒
a
=
1
⇒
d
d
r
(
α
r
10
−
β
r
5
−
3
)
=
0
⇒
d
d
r
(
α
r
−
10
−
β
r
−
5
−
3
)
=
0
⇒
−
10
α
r
−
11
+
5
β
r
−
6
−
0
=
0
⇒
10
α
r
−
11
=
5
β
r
−
6
⇒
2
α
r
−
11
=
β
r
−
6
⇒
2
α
β
=
r
−
6
r
−
11
=
r
5
⇒
r
=
(
2
α
β
)
1
∕
5
⇒
a
=
1
© examsnet.com
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