The half life of a radioactive nucleus is 50 days. The time interval (t2-t1)  between the time t2  when 23 of it has decayed and the time t1 when of it had decayed 13  is:

# The half life of a radioactive nucleus is 50 days. The time interval between the time ${t}_{2}$  when of it has decayed and the time when of it had decayed is:

1. A
60 days
2. B
15 days
3. C
30 days
4. D
50 days

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### Solution:

Concept: From radioactive decay law, N = ${N}_{0}{e}^{-\mathit{\lambda t}}$ where ${N}_{0}$ be the amount of nuclei at t = 0 and N be the left nuclei under decay at any time t.
At = $\frac{{N}_{0}}{3}$
And at ${t}_{1}⇒$ $N={N}_{0}-\frac{{N}_{0}}{3}$ = $\frac{2{N}_{0}}{3}$
Now,  ………(1)
And ………(2)
$⇒$ = 2
$⇒$ = 50 days
Hence, the correct option is 4.

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