Question

Ten percent of a radioactive sample has decayed in 1 day. after 2 day the decayed percentage of nuclei will be

Answer 1

a/c to question,

10% of a radioactive sample has decayed in 1 day.

Let initially radioactive sample is $N_0$

after one day, radioactive sample remains, N = $N_0-\frac{10}{100}\times N_0$

= $0.9N_0$

using rate equation of radioactive,

$N=N_0e^{-\lambda t}$

$0.9N_0=N_0e^{-\lambda 1}$

$\lambda=-ln(0.9)$.......(1)

Let after 2 days , radioactive sample remains N'

then, N' = $N_0e^{-\lambda 2}$

from equation (1),

N' = $N_0e^{2ln(0.9}$

N' = $N_0e^{ln(0.9)^2}$

N' = $0.81N_0$

hence, 81% radioactive sample remains in 2 days .

so, 19% of radioactive sample has decayed in 2 days.