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 100 m is \(\displaystyle \frac {\text {Distance}}{\text {speed}}= \frac{100}{2500}=0.04 \: sec\)
\(\displaystyle \frac{dN}{N}=\lambda .dt\)
The fraction of neutron will decay before they travel a distance of 10 meters is \(\displaystyle \frac{dN}{N}=\frac{0.693}{700}\times 0.04=3.96\times 10^{-5}\)