Chemistry, asked by ayushimttal7929, 1 year ago

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

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Answered by abhi178
37
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.
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