Question

The half-life of radium is $1500$ years. In how many years will $1g$ of pure radium be reduced to one centigram?

• A. $3.928\times {10}^{2}years$
• B. $9.972\times {10}^{2}years$
• C. $99.927\times {10}^{2}years$
• D. $0.927\times {10}^{2}years$

Answer 1

Answer: (B)

$9.972\times {10}^{2}years$

$t_{1/2}=1500$ years
$\lambda =\frac{1}{t_{1/2}}$
$1gms\to 1cgm=0.01gms$

$N\left(t\right)=N_o{e}^{-\lambda t}$

$0.01=e^{\frac{-ln2}{1500}t}$
On solving

$t=9.972\times {10}^{2}years$