Question

At a certain instant, a piece of radioactive material contains ${10}^{12}$ atoms. The half life of material is 30 days. The number of disintegrations per second are :

• A. $2.674\times {10}^{5}dps$
• B. $2.245\times {10}^{4}dps$
• C. $2.798\times {10}^{6}dps$
• D. none of these

Answer 1

The correct option is A $2.674\times {10}^{5}dps$

$t_{1/2}=30days;N_0={10}^{12}atoms$
The disintegration rate in 1 s means differential rate of disintegration.
$-\frac{dN}{dt}=K{N}_0$
$=\frac{0.693}{30\times 24\times ,6060}\times {10}^{12}$
$=2.674\times {10}^{-6}g$