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 |
| \[\frac{N}{{{N}_{0}}}={{\left( \frac{1}{2} \right)}^{n}}\] |
| or \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] |
| \[=4\times {{10}^{10}}{{\left( \frac{1}{2} \right)}^{3}}\] |
| \[=4\times {{10}^{10}}\times \frac{1}{8}=0.5\times {{10}^{10}}\] |
| Thus, number of nuclei decayed after 30 days |
| \[={{N}_{0}}-N=4\times {{10}^{10}}-0.5\times {{10}^{10}}=3.5\times {{10}^{10}}\] |
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