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There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half life of neutrons is 700 seconds, what fraction of neutrons will decay before they travel a distance of 10 m ?

There is a stream of neutrons with a kinetic energy of 0.0327 eV. If the half life of neutrons is 700 seconds, what fraction of neutrons will decay before they travel a distance of 10 m ?

Grade:11

1 Answers

Kevin Nash
askIITians Faculty 332 Points
9 years ago
Hello Student,
Please find the answer to your question
K.E. = 0.0327 eV = 0.327 x 1.6 x 10-19 J
½ mn v2n = 0.0327 x 1.6 x 10-19
⇒ vn [2 x 0.0327 x 1.6 x 10-19/ 1.675 x 10-27]1/2
⇒ vn = 0.25 x 104 m/s
Time taken by the neutron to travel 10 m will be
t = d / vn = 10 / 0.25 x 104 = 4 x 10-3 s
Let the number of neutron initially be a.
λ = 0.693 / t1 / 2 = 0.693 / 700 s-1
We know that
t = 2.303 / λ log a / a – x
⇒ 4 x 10-3 / 2.303 x 0.693 / 700 = 1=log10 a / a – x
⇒ log10 a / a – x = 1.72 x 10-6 ⇒ a / a – x = 1.000004
⇒ x / a = 3. 96 x 10-6
Thanks
Kevin Nash
askIITians Faculty

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