The half life of a radioactive material is ‘T’ second.

The half life of a radioactive material is ‘T’ second. If 80% of the sample decay after time ‘t’ second, then find out the time when 90% of the sample decay.

Report

Question

Let t’ be the time taken to decay 90% of the sample

According to law of radioactive decay,

N=N0e-t( N is the number of sample left, and N0is the number of sample at the beginning)

lnN0N=t ( is decay constant which is, =ln2T)

According to the question, 80% of the sample decay after time ‘t’ second, so 20% of the radioactive sample is left after ‘t’ second. Hence,

ln10020=ln2Tt (=ln2T)

ln5=ln2Tt

t=ln5ln2T

When 90% of the sample is decayed, then 10% of the radioactive sample is left. Hence time taken is t’,

ln10010= ln2Tt'

ln10=ln2Tt'

t'=ln10ln2T

=ln(52)ln2T

=ln5+ln2ln2T

=ln5ln2T+T

=t+T

Hence, the correct option is A, i.e. T+t

solved 5

wordpress 4 mins ago 5 Answer 70 views +22