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 ${\displaystyle \frac{1}{2}m{u}^2=0.0327\times 1.6\times {10}^{-19}J}$        --{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 ${\displaystyle u^2=\frac{2\times 0.0327\times 1.6\times {10}^{-19}}{1.675\times {10}^{-27}}}$    =625×10⁴ 

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

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

${\displaystyle \frac{dN}{N}=\lambda .dt}$

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