A) \[2.4\times {{10}^{-6}}\]
B) \[4\times {{10}^{-6}}\]
C) \[2\times {{10}^{-5}}\]
D) \[1.5\times {{10}^{-6}}\]
Correct Answer: B
Solution :
[b] Speed of neutrons is given by \[\frac{1}{2}m{{v}^{2}}=0.0327\times 1.6\times {{10}^{-19}}\] \[\therefore \,\,\,\,\,\,\,\,\,\,\,{{v}^{2}}=\frac{2\times 0.0327\times 1.6\times {{10}^{-19}}}{1.627\times {{10}^{-27}}}=6.25\times {{10}^{4}}\] or \[v=2500\,m/s\] With this speed, the time taken by the neutrons to travel a distance of 10 m is \[\Delta t=\frac{10}{2500}=4\times {{10}^{-3}}s\] This time is very small compared to the half-life, hence the fraction of neutrons decayed in time \[\Delta t\] can be calculated as \[\frac{\Delta N}{N}=\lambda \Delta t\]But, \[\lambda =\frac{0.693}{{{T}_{1/2}}}\] \[\therefore \,\,\,\frac{\Delta N}{N}=\frac{0.693}{{{T}_{1/2}}}\Delta t=\frac{0.693}{693}\times (4\times {{10}^{-3}})=4\times {{10}^{-6}}\]
You need to login to perform this action.
You will be redirected in
3 sec
