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}} $