Question

There is a stream of neutrons with the kinetic energy of 0.0327 eV. If half-life period of a neutron is 700 sec, the fraction of neutron will decay before they travel a distance of 100 meters:

• A. $7.47\times {10}^{-5}$
• B. $3.96\times {10}^{-5}$
• C. $5.25\times {10}^{-5}$
• D. None of these

Answer 1

Answer: (B)

$3.96\times {10}^{-5}$

The kinetic energy of neutron is $\frac{1}{2}m{u}^2=0.0327\times 1.6\times {10}^{-19}J$

Note: Here the unit eV is converted to J by multiplying with $1.6\times {10}^{-19}$

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

Therefore $u^2=\frac{2\times 0.0327\times 1.6\times {10}^{-19}}{1.675\times {10}^{-27}}$

$=625\times {10}^4$

$\therefore$, the speed of neutrons is $u=2500m/sec$

Time taken to travel 100 m is $\frac{\text{Distance}}{\text{speed}}=\frac{100}{2500}=0.04sec$

Now, $\frac{dN}{N}=\lambda .dt$

The fraction of neutron will decay before they travel a distance of 100 meters is:

$\frac{dN}{N}=\frac{0.693}{700}\times 0.04=3.96\times {10}^{-5}$.