Question

The half life of a radioactive substance is $34.65$ minute. If ${10}^{22}$ atoms are active at any instant of time, then it; activity will be

• A. $1\times {10}^{18}$ $disintegrations/sec$
• B. $2\times {10}^{18}$ $disintegrations/sec$
• C. $3.33\times {10}^{18}$ $disintegtations/sec$
• D. $4\times {10}^{18}$ $disintegrations/sec$

Answer 1

The correct option is C $3.33\times {10}^{18}$ $disintegtations/sec$

Amount active is $N={10}^{22}atoms$

Half life is $34.65\times 60=2079s$

decay constant $\lambda =0.693/2079=3.33\times {10}^{-4}persec$

So activity will be $N\times \lambda =3.33\times {10}^{18}disintegrations/sec$