A) \[\text{3 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}\]
B) \[\text{9 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}\]
C) \[\text{1 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}\]
D) \[\text{6 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-3}}}\text{/day}\]
Correct Answer: B
Solution :
The time required for the number of parent nuclei to fall to 50% is called half-life \[{{T}_{1/2}}\] and may be related to \[\lambda \]as follows. Since, \[0.5\,{{N}_{0}}={{N}_{0}}{{e}^{-{{T}_{1//2}}}}\] we have, \[\lambda {{T}_{1/2}}=\ln (2)=0.693\] or \[{{T}_{1/2}}=\frac{0.693}{\lambda }\] or \[\lambda =\frac{0.693}{{{T}_{1/2}}}\] Given, \[{{T}_{1/2}}=77\] days \[\therefore \] \[\lambda =\frac{0.693}{77}=9\times {{10}^{-3}}/days\]
You need to login to perform this action.
You will be redirected in
3 sec
