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JEE Main 31-Aug-2021 Shift 2 Solved Paper
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Question : 8
Total: 90
Consider two separate ideal gases of electrons and protons having same number of particles. The temperature of both the gases are same. The ratio of the uncertainty in determining the position of an electron to that of a proton is proportional to
[31 Aug 2021 Shift 2]
(
m
p
m
e
)
3
2
√
m
e
m
p
√
m
p
m
e
m
p
m
e
Validate
Solution:
At same temperature kinetic energy of proton and electron are same
KE
p
=
KE
e
⇒
p
p
2
2
m
p
=
p
e
2
2
m
e
p
p
2
p
e
2
=
m
p
m
e
...(i)
Using uncertainty in determining the position,
Δ
x
≈
h
Δ
p
Ratio,
∴
Δ
x
e
Δ
x
p
=
Δ
p
p
Δ
p
e
=
√
m
p
m
e
[from Eq. (i)]
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