CBSE Class 12 Physics 2019 Outside Delhi Set 1 Paper

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Question : 21
Total: 27
Why is it difficult to detect the presence of an antineutrino during β-decay? Define the term decay constant of a radioactive nucleus and derive the expression for its mean life in terms of the decay constant.
OR
(a) State two distinguishing features of nuclear force.
(b) Draw a plot showing the variation of potential energy of a pair of nucleons as a function of their separation. Mark the regions on the graph where the force is (i) attractive, and (ii) repulsive.
Solution:  
Reason for difficulty in detecting presence of antineutrino during β decay
Define decay constant of radioactive nucleus
Derive expression for mean life in terms of decay constant
● Penetrating power is high
● Do not interact with matter (weak interaction) (any one)
● Decay constant is the reciprocal of the time duration in which undecayed radioactive nuclei reduce to 1e times the nuclei present initially.
τ=
total life time of all nuclei
total number of nuclei

τ=
0
tdN
N0

τ=
0
t(N0λελtdt)
N0
=λteλtdt

τ=
1
λ

OR
(a) Stating distinguishing feature of nuclear force.
(b) Drawing a plot showing variation of potential energy.
(c) Marking the regions.
(1) Short rang force
(2) Strongest force
(3) Attractive in nature
(4) Does not depend on charge (any two)
(b)
r<r0 : repulsive force
r>r0: attractive force
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