Question

The half-life of radium is $1620$ yr and the atomic weight is $226$ kg per kilo mol. The number of atoms that will decay from its $1g$ sample per second will be (Take Avogadro's number $N_A=6.023\times {10}^{23}$ atom/kilo mol).

• A. $3.61\times {10}^{10}$
• B. $3.11\times {10}^{15}$
• C. $3.6\times {10}^{12}$
• D. $3.1\times {10}^{15}$

Answer 1

The correct option is A $3.61\times {10}^{10}$

$\frac{dN}{dt}=\lambda N$

$\lambda =\frac{0.6931}{t_1/2}=\frac{0.6931}{1620\times 366\times 24+60\times 60}$

$N=\frac{6.023\times {10}^{23}}{226}$

$\frac{dN}{dt}=\frac{0.6931\times 6.023\times {10}^{23}}{1620\times 365\times 24\times 60\times 60\times 226}=3.61\times {10}^{10}$