Question

The activity of ratio altitude $({{X}^{100}})$ is 6.023 curie. If its disintegration constant is $3.7\times {{10}^{4}}{{\sec }^{-1}},$ the mass of X is :

• A. ${{10}^{-23}}g$
• B. ${{10}^{-15}}g$
• C. ${{10}^{-16}}g$
• D. ${{10}^{-14}}g$

Answer 1

The Correct Option is B

We know that 1 Curie $3.7\,\,\times \,\,{{10}^{10}}$ disintegration per sec So, activity $=6.023\times 3.7\times {{10}^{10}}\,\text{dps}$ $\lambda =3.7\times {{10}^{14}}\,{{\sec }^{-1}}$ $N=\frac{Activity}{\lambda }=\frac{6.023\times 3.7\times {{10}^{-10}}}{3.7\times {{10}^{4}}}$ $=6.023\times {{10}^{6}}\text{atoms}$ $\because$ Weight of $6.023\times {{10}^{23}}$ atoms = 100 g $\therefore$ Weight of $6.023\times {{10}^{6}}$ atoms will be $=\frac{100\times 6.023\times {{10}^{6}}}{6.023\times {{10}^{23}}}={{10}^{-15}}\,g$