A) \[4.6\times {{10}^{-}}^{5}\]
B) \[3.9\times {{10}^{-}}^{6}\]
C) \[9.2\times {{10}^{-}}^{5}\]
D) \[7.8\times {{10}^{-}}^{6}\]
Correct Answer: B
Solution :
[b]: Kinetic energy of neutron = 0.0327 eV or \[K=0.0327\times 1.6\times {{10}^{-19}}J\] or \[\frac{1}{2}m{{v}^{2}}=0.0327\times 1.6\times {{10}^{-19}}\] or\[{{v}^{2}}=\frac{2\times 0.0327\times 1.6\times {{10}^{-19}}}{1.675\times {{10}^{-27}}}\] or\[{{v}^{2}}=0.0625\times {{10}^{8}};v=0.25\times {{10}^{4}}m{{s}^{-1}}\] \[\therefore \]Time taken\[=\frac{\text{distance}}{\text{velocity}}=\frac{10}{0.25\times {{10}^{4}}}\] or\[t=4\times {{10}^{-3}}s\] \[\therefore \]Fraction that decays\[=\frac{N}{{{N}_{0}}}=(1-{{e}^{-\lambda t}})\] \[=1-\left\{ -\left( \frac{0.693}{700} \right)\times 4\times {{10}^{-3}} \right\}=3.9\times {{10}^{-6}}\]
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