The kinetic energy of neutron is \(\displaystyle \frac{1}{2}mu^2=0.0327\times 1.6\times 10^{-19}J\) --{the unit eV is converted to J by multiplying with 1.6×10^{−19}}

The mass of neutron is \( 1.675 \times 10^{-27 } \)

Therefore \(\displaystyle u^2=\frac{2 \times0.0327 \times 1.6 \times 10^{-19}}{1.675 \times 10^{-27} }\) =625×10^{4 }

∴, the speed of neutrons is u=2500m/sec

Time taken to travel 10 m is \(\displaystyle \frac {\text {Distance}}{\text {speed}}= \frac{10}{2500}=0.004 \: sec\)

\(\displaystyle \frac{dN}{N}=\lambda .dt\)

The fraction of neutron will decay before they travel a distance of 10 meters is \(\displaystyle \frac{dN}{N}=\frac{0.693}{700}\times 0.004=3.96\times 10^{-6}\)

Get Your advertisement on Brainiak.in Buy Adspace