Question

The half-life of $Ra ^{226}$ is 1620 years. Then the number of atoms decay in one second in $1 g$ of radium (Avogadro number $\left.=6.023 \times 10^{23}\right)$

• A. $4.23 \times 10^{9}$
• B. $3.16 \times 10^{10}$
• C. $3.61 \times 10^{10}$
• D. $2.16 \times 10^{10}$

Answer 1

Answer: (C)

The number of atoms decay in one second
$\frac{d N}{d t} =\lambda N $
$=\frac{0.693}{1620 \times 365 \times 86 \times 400} \times \frac{6.023 \times 10^{23}}{226}$
$=3.61 \times 10^{10}$