Question

The half life of radium $Ra ^{226}$ 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 $\frac{ d N }{ dt }=\lambda N$
$=\frac{0.693}{1620 \times 3.16 \times 10^{7}} \times \frac{6.023 \times 10^{23}}{226}$
$=3.16 \times 10^{10} s ^{-1}$
$\approx 3 \times 10^{10} s ^{-1}$