Question

The half-life of radium is 1620 years and its atomic weight is 226 kg per kilomol. 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)

$3.61\,\times {{10}^{10}}$

Answer 2

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 $\frac{dN}{dt}=\frac{0.693\times 6.023\times {{10}^{23}}}{1620\times 365\times 24\times 60\times 226}$ $=3.61\times {{10}^{10}}$