Question

The mass of $R{a}^{226}$ having an activity of 1 curie is ($T_{1/2}$ of $R{a}^{226}$ is $1622yr$)

• A. $234g$
• B. $3.2\times {10}^{-8}g$
• C. $1.438\times {10}^{-11}g$
• D. $432g$

Answer 1

The correct option is B $3.2\times {10}^{-8}g$

$\begin{array}{c}\text{Given}\\ \text{Activity of}R{a}^{226}=1\text{curie}\\ \text{let mass present}=\text{w gram}\end{array}$

$\begin{array}{c}\text{we know}\\ \text{Activity}\left(A\right)=\lambda N\end{array}$ $\therefore N=\text{mole}\times {\text{N}}_a$

$N=\frac{\text{mass}}{\text{atomic weight}}\times N_a$

$\begin{array}{c}\text{Now,}\\ \begin{array}{cc}& A=\lambda \cdot \frac{\text{w gram}}{226}\times 6.022\times {10}^{23}\\ T_{1/2}& =1622\text{yoar}\\ \lambda & =\frac{0.693}{T_{1/2}}\\ \therefore \lambda & =\frac{0.693}{1622}\end{array}\end{array}$

$\text{and}1\text{curie}=3.7\times {10}^{10}\left(Bq\right)\text{(in}SI\text{unit)}$

$3.7\times {10}^{10}=\frac{0.693}{1622}\times \left(\frac{\omega }{226}\right)\times 6.022\times {10}^{23}$

$\omega =3.2\times {10}^{-8}gram$