Question

A radioactive sample with a half life of 1 month has the label : 'Activity = 2 micro curies on 1-8-1991'. What would be its activity two months earlier?

• A. 1.0 micro curie
• B. 0.5 micro curie
• C. 4 micro curie
• D. 8 micro curie

Answer 1

The correct option is D 8 micro curie

$\begin{array}{c}\text{Given,}\\ \text{Activity of same on}(1-8-1991)=2\left(\mu \text{courie}\right)\\ T_{1/2}\text{(half life)}=1\text{month}\end{array}$

$\begin{array}{c}\text{Activity after time}t=A_0{\left(\frac{1}{2}\right)}^n\\ \text{where}{A}_0=\text{initial Acitvity}\\ \begin{array}{cc}n& =\frac{\text{Time}}{\text{half life}}\\ n& =\frac{2\text{month}}{1\text{month}}\text{(given)}\\ n& =2\end{array}\end{array}$

$\begin{array}{c}{A}_t=2{\left(\frac{1}{2}\right)}^2\\ A_t=\frac{1}{2}\\ A_t=0.5\text{micro courie}\end{array}$