A) \[0.5\times {{10}^{10}}\]
B) \[2\times {{10}^{10}}\]
C) \[3.5\times {{10}^{10}}\]
D) \[1\times {{10}^{10}}\]
Correct Answer: C
Solution :
Number of half-lives \[n=\frac{t}{T}=\frac{30\,days}{10\,days}=3\] So, number of undecayed radioactive nuclei \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] \[orN={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[=4\times {{10}^{10}}{{\left( \frac{1}{2} \right)}^{3}}\] \[=4\times {{10}^{10}}\times \frac{1}{8}=0.5\times {{10}^{10}}\] Thus, number of nuclei decayed after 30 days \[={{N}_{0}}-N=4\times {{10}^{10}}-0.5\times {{10}^{10}}=3.5\times {{10}^{10}}\]
You need to login to perform this action.
You will be redirected in
3 sec
