Question

Determine the half-life (in h) of a radioactive sample that has an activity of 10.3 mCi at some time and 7 mCi 1.60 h later. (I got 4.15 hours but it was incorrect)

Answer 1

activity in becquerel=N*lambda

where N is number of undecayed nuclei

lambda=decay constant

let at t=0, activity=10.3 mCi=10.3*0.001*3.7*10^10=3.811*10^8 Bq

==>N0*lambda=3.811*10^8 Bq

at t=1.6 hours, activity=7 mCi=2.59*10^8 Bq

N1*lambda=2.59*10^8

as the decay is exponential in nature,

N1=N*exp(-lambda*t)

==>N1=N*exp(-lambda*1.6)

==>-lambda*1.6=ln(N1/N)=-0.38623

==>lambda=0.2414

as half life=ln(2)/lambda

=2.8714 hours

hence half life of the sample is 2.8714 hours.