The half- life periods of a radioisotopes is 20 seconds starting with 0.2 g of the isotope, the amount left after 2 minutes is

Half life period of a radioisotopes, ${\text{t}}_{1/2}=20\sec$

Total period of time for decaying radioisotope, $t=2\min =120\sec$

From first order kinetics equation, rate constant ‘k’ is$\text{k}=\frac{0.693}{{\text{t}}_{1/2}}=\frac{0.693}{20\sec }=0.034{\sec }^{-1}$

Use the following formula to find amount of radioisotope left after time, ‘t’ is ${\text{N}}_{\text{t}}={\text{N}}_0.{\text{e}}^{-\text{kt}}$

${\text{N}}_{\text{t}}=0.2\times {\text{e}}^{-(0.034\times 120)}$

$\therefore {\text{N}}_{\text{t}}=0.00312\text{\hspace{0.17em}g}\left(\text{or}\right)3.12\text{\hspace{0.17em}mg}$