Question

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 ?

Answer 1

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 \(\displaystyle u^2=\frac{2 \times0.0327 \times 1.6 \times 10^{-19}}{1.675 \times 10^{-27} }\)    =625×10⁴ 

∴, 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  \(\displaystyle \frac{dN}{N}=\frac{0.693}{700}\times 0.004=3.96\times 10^{-6}\)