Question

At any given time a piece of radioactive material $(t_{1/2}=30days)$ contains ${10}^{12}$ atoms. Calculate the activity of the sample in dps?

• A. $3.67\times {10}^{5}dps$
• B. $1.67\times {10}^{5}dps$
• C. $2.67\times {10}^{5}dps$
• D. $4.67\times {10}^{5}dps$

Answer 1

The correct option is C $2.67\times {10}^{5}dps$

The decay constant is calculated from the half life period
$\lambda =\frac{0.693}{t_{1/2}}k=\frac{0.693}{30\times 24\times 3600}=2592000s^{-1}$
The activity of the sample is
$-\frac{dN}{dt}=N\lambda -\frac{dN}{dt}={10}^{12}\times 2592000=2.67\times {10}^5$ dps