SATHEE: Modern Physics 3 Question 42

Modern Physics 3 Question 42

41. There is a stream of neutrons with a kinetic energy of $0.0327 e V$ . If the half-life of neutrons is $700 s$ , what fraction of neutrons will decay before they travel a distance of 10 $m$ ?

$(1986, 6$ M)

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Answer:

Correct Answer: 41. $3.96 \times 10^{- 6}$

Solution:

Speed of neutrons $= \sqrt{\frac{2 K}{m}}$ From $K = \frac{1}{2} m v^{2}$

$or v = \sqrt{\frac{2 \times 0.0327 \times 1.6 \times 10^{- 19}}{1.675 \times 10^{- 27}}}$

$\approx 2.5 \times 10^{3} m / s$

Time taken by the neutrons to travel a distance of $10 m$ :

$t = \frac{d}{v} = \frac{10}{2.5 \times 10^{3}} = 4.0 \times 10^{- 3}$

Number of neutrons decayed after time

$t : N = N_{0} (1 - e^{- λ t})$

$∴$ Fraction of neutrons that will decay in this time interval

$\begin{aligned} = \frac{N}{N_{0}} = (1 - e^{- λ t}) = 1 - e^{- \frac{\ln (2)}{700} \times 4.0 \times 10^{- 3}} \\ = 3.96 \times 10^{- 6} \end{aligned}$

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Modern Physics 3 Question 42

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

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41. There is a stream of neutrons with a kinetic energy of $0.0327 e V$ . If the half-life of neutrons is $700 s$ , what fraction of neutrons will decay before they travel a distance of 10 $m$ ?