Nuclei - Result Question 87
89. The activity of a radioactive sample is measured as 9750 counts per minute at $t=0$ and as 975 counts per minute at $t=5$ minutes. The decay constant is approximately
[1997]
(a) 0.922 per minute
(c) 0.461 per minute
(b) 0.691 per minute
(d) 0.230 per minute
Show Answer
Answer:
Correct Answer: 89. (c)
Solution:
(c) $\frac{d N}{d t}=K N$ $9750=K N_0$ $975=K N$
(1)
(2)
Dividing (1) by (2)
$\frac{N}{N_0}=\frac{1}{10}$
$K=\frac{2.303}{t} \log \frac{N_0}{N}=\frac{2.303}{5} \log 10$
$=0.4606=0.461$ per minute
