Question

At a certain instant a piece of radioactive material contains ${10}^{12}$ atoms. The half life of material is 30 days. Calculate the no. of disintegrations in one second.

• A. $2.674\times {10}^{5}dps$
• B. $4.348\times {10}^{5}dps$
• C. $26.74\times {10}^{5}dps$
• D. None of these

Answer 1

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

The decay constant $\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{30}=0.0231/day$

$-\frac{dN}{dt}=N\lambda$

$-\frac{dN}{dt}={10}^{12}\times 0.0231=2.31\times {10}^{10}$ disintegrations per day

$-\frac{dN}{dt}=\frac{2.31\times {10}^{10}}{24\times 3600}=2.674\times {10}^{5}dps$