Physics - Modern Physics Question with Solution | TestHub

From the given kinetic energy of the neutrons we first calculate their velocity. Thus

$\frac{1}{2}{\text{mv}}^2=0\text{.}0327\times 1\text{.}6\times 10^{-19}$

∴$v^2=\frac{2\times 0\text{.}0327\times 1\text{.}6\times 10^{-19}}{1\text{.}675\times 10^{-27}}=625\times 10^4$

or       v = 2500 m/s

With this speed, the time taken by the neutrons to travel a distance of 10 m is,

$\Delta t=\frac{10}{2500}=4\times 10^{-3}s$

The fraction of neutrons decayed in time Δt second is,

$\frac{\Delta N}{N}=\lambda \Delta t$

Also,$\lambda =\frac{0\text{.}693}{T_{1/2}}$

$\therefore \; \; \; \frac{\Delta N}{N}=\frac{0\text{.}693}{T_{1/2}}\Delta t=\frac{0\text{.}693}{700}\times \left(4\times 10^{-3}\right)=3\text{.}96\times 10^{-6}$