Question

The half life of $R{a}^{226}$ is $1620$ years. Then the number of atoms decay in one second in $1$ gm of radium:

(Avogadro number $=6.023\times {10}^{23})$

• 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

The correct option is C $3.61\times {10}^{10}$

Half life: $t_{\frac{1}{2}}=1620$ years

$\Rightarrow \lambda =\frac{ln2}{t_{\frac{1}{2}}}$

$\Rightarrow \frac{dN}{dt}=\lambda N$

$=\frac{0.693}{1620\times 365\times 86400}\times \frac{6.023\times {10}^{23}}{226}$

$=3.61\times {10}^{10}$