Question

A sample contains 16g of a radioactive material, the half life of which is two days. After 32 days, the amount of radioactive material left in the sample is

• A. less than $1mg$
• B. $\frac{1}{4}$g
• C. $\frac{1}{2}$g
• D. $1g$

Answer 1

The correct option is A less than $1mg$

Given,

$N_0=16g$

Half-life time, $T=2day$

Time, $t=32day$

The amount of radioactive sample after time t,

$N=N_0(1/2{)}^{t/T}$

$N=16(1/2{)}^{32day/2day}=16(1/2{)}^{16}gm$

$N=2.441\times {10}^{-4}gm$

The amount of radioactive sample after 32 days is less than $1gm$.

The correct option is A.