The half life of a radioactive nucleus is 50 days. The time interval (t_2-t_1) between the time t_2 when (2)/(3) of it has decayed and the time t_1 when (1)/(3) of it had decayed is

Correct answer: B. 50 days Active fraction at instant t_2 , 1 2^ t_2 / T_ 1/2 =(1)/(3) Active fraction at instant t_1 , aligned 1 2^ t_1 / T_ 1/2 & =(2)/(3) 2^ t_2 / T_ 1/2 2^ t_1 / T_ 1/2 & =2 t_2-t_1=T_ 1/2 & =50 days aligned

NEET 2012

Exam: NEET
Year: 2012
Subject: Physics
Chapter: Nuclear Physics

NEET 2012 · Physics · Nuclear Physics

The half life of a radioactive nucleus is 50 days. The time...

The half life of a radioactive nucleus is 50 days. The time interval

\left(t_2-t_1\right)

between the time

t_2

when

\frac{2}{3}

of it has decayed and the time

t_1

when

\frac{1}{3}

of it had decayed is

Options

A30 days
B50 days
C60 days
D15 days

Correct answer

B. 50 days

Step-by-step solution

Active fraction at instant

t_2

\frac{1}{2^{t_2 / T_{1/2}}}=\frac{1}{3}

Active fraction at instant

t_1

\begin{aligned}\frac{1}{2^{t_1 / T_{1/2}}}& =\frac{2}{3}\\ \frac{2^{t_2 / T_{1/2}}}{2^{t_1 / T_{1/2}}}& =2 \\ t_2-t_1=T_{1/2} & =50 \text{ days } \end{aligned}

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