Question

The half life of radium $R{a}^{226}$ is 1620 years. How many atoms decay in 1 second in a 1 gram sample of radium?

• A. $4\times 10^{10}{s}^{-1}$
• B. $3\times 10^{10}{s}^{-1}$
• C. $3\times 10^{-10}{s}^{-1}$
• D. $3\times 10^{10}s$

Answer 1

Answer: (B)

$N=\frac{6.023\times 10^{23}}{226}$
$\lambda =\frac{0.693}{T}=\frac{0.693}{1620\times 3.16\times 10^7}$
$\therefore$ No. of disintegration per second $\frac{dN}{dt}=\lambda N$
$=\frac{0.693}{1620\times 3.16\times 10^7}\times \frac{6.023\times 10^{23}}{226}$
$=3.16\times 10^{10}{s}^{-1}$
$\approx 3\times 10^{10}{s}^{-1}$