Question

The half-life of radium is $1620$ years and its atomic weight is $226$. The number of atoms that will decay from its $1g$ sample per second will be

• A. $3.6\times {10}^{10}$
• B. $3.6\times {10}^{12}$
• C. $3.1\times {10}^{15}$
• D. $31.1\times {10}^{15}$

Answer 1

The correct option is A $3.6\times {10}^{10}$

$\frac{dN}{dt}=-\lambda N$
$\lambda =\frac{ln2}{t_{1/2}}$
$\frac{dN}{dt}=-\frac{ln2}{1620\times 365\times 24\times 3600}\frac{1}{226}\times (6.023\times {10}^{23})=3.6\times {10}^{10}$