Nuclei - Result Question 91
93. The count rate of a Geiger Muller counter for the radiation of a radioactive material of half-life 30 minutes decreases to $5 sec^{-1}$ after 2 hours. The initial count rate was
(a) $20 sec^{-1}$
(b) $25 sec^{-1}$
(c) $80 sec^{-1}$
(d) $625 sec^{-1}$
[1995]
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Answer:
Correct Answer: 93. (c)
Solution:
- (c) Half-life $=30$ minutes; Rate of decrease $(N)=5$ per second and total time $=2$ hours $=120$ minutes. Relation for initial and final count rate
$\frac{N}{N_0}=(\frac{1}{2})^{\text{time/half-life }}=(\frac{1}{2})^{120 / 30}=(\frac{1}{2})^{4}=\frac{1}{16}$.
Therefore, $N_0=16 \times N=16 \times 5=80 s^{-1}$.
