Q137 / 160 · TS EAMCET 2012 · Physics

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

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

Solution

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

Hence, the correct answer is option: 'C'.

Relevant Questions