Question

The half-life of radium is 1620 years and its atomic weight is 226 kg per kilo mol. The number of atoms that will decay from its 1 gm sample per second will be : (Avogadros number $N=6.023\times {10}^{23}$ atoms/mol)

• A. $3.61\times {10}^{10}$
• B. $3.6\times {10}^{12}$
• C. $3.11\times {10}^{15}$
• D. $31.1\times {10}^{15}$

Answer 1

Answer: (A)

From the formula $\frac{dN}{dt}=\lambda N$ ??.(i) and $\lambda =\frac{0.693}{T_{1/2}}$ $=\frac{0.693}{1620\times 365\times 24\times 60\times 60}$ ??(ii) and $N=\frac{6.023\times {10}^{23}}{226}$ ?..(iii) Now from equations (ii) and (iii), putting the values of K and N in equation (i), we get $\frac{dN}{dt}=\frac{0.693\times 6.023\times {10}^{23}}{1620\times 365\times 24\times 60\times 60\times 226}$ $=3.61\times {10}^{10}$