A) 30 min
B) 90 min
C) 45 min
D) 60 min
Correct Answer: A
Solution :
Key Idea: The radioactive half-life of a substance is the period of time over which the number of radioactive nuclei decreases by a factor one-half. If number of atoms in a substance is \[{{\text{N}}_{\text{0}}}\text{,}\] and N be the number of atoms left after n half-lives, then \[N={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] Mass left after two hours \[=\frac{{{N}_{0}}}{16}\] \[\therefore \] \[\frac{{{N}_{0}}}{16}={{N}_{0}}{{\left( \frac{1}{2} \right)}^{n}}\] \[\Rightarrow \] \[{{\left( \frac{1}{2} \right)}^{n}}=\frac{1}{16}\] \[\Rightarrow \] \[n=4\] Hence, half-life period\[=\frac{120\,\min }{4}=30\,\min .\]
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