MCQ
A radioactive element emits $200$ particles per second. After three hours $25$ particles per second are emitted. The half life period of element will be ..........$minntes$
- A$50$
- ✓$60 $
- C$70$
- D$80$
✓
Answer
Correct option: B.
$60 $
b
(b) $R = \frac{{dN}}{{dt}} \propto N$
(b) $R = \frac{{dN}}{{dt}} \propto N$
$\Rightarrow \frac{{{R_2}}}{{{R_1}}} = \frac{{{N_2}}}{{{N_1}}}$
But $\frac{{{N_2}}}{{{N_1}}} = {\left( {\frac{1}{2}} \right)^{{t_{1/2}}}}$
$\Rightarrow \frac{{25}}{{200}} = \frac{1}{8} = {\left( {\frac{1}{2}} \right)^3}$
$\Rightarrow \frac{t}{{{t_{1/2}}}} = 3$
$\therefore {t_{1/2}} = \frac{t}{3} = \frac{3}{3} = 1\;hour = 60\,minutes$
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