The half life of a radioactive nucleus is

50 days. The time interval $\left({\mathrm{t}}_{2}-{\mathrm{t}}_{1}\right)$ between

the time ${\mathrm{t}}_{2}$ when $\frac{2}{3}$ of it has decayed and

the time ${\mathrm{t}}_{1}$ when $\frac{1}{3}$ of it had decayed is

(a) 30 days

(b) 50 days

(c) 60 days

(d) 15 days

Active fraction at instant ${\mathrm{t}}_{2}$,

$\frac{1}{{2}^{{}^{{\mathrm{t}}_{2}/{\mathrm{T}}_{1/2}}}}=\frac{1}{3}$

Active fraction at instant ${\mathrm{t}}_{1}$,

$\frac{1}{{2}^{{\mathrm{t}}_{1}/{\mathrm{T}}_{1/2}}}=\frac{2}{3}$

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