A sample consisting of 86x1012 atoms was found to have decay

A sample consisting of 8.6x10^12 atoms was found to have decayed to 2.3x10^12 atoms after 5 years.

a)what is the half life of the radioactive sample in years?

b)what is the activity (in microcuries) after the 5 year decay period?

Solution

Here ,

initial number of atoms , No = 8.6 *10^12

final number of atoms , N = 2.3 *10^12

time ,t = 5 years

a) let the half life is t0.5

as N = No * (0.5)^(t/t0.5)

2.3*10^12 = 8.6 *10^12 * (0.5)^(5/t0.5)

sovling

t0.5 = 2.63 years

the half life is 2.63 years

b)

final activity = ln(2)/t0.5 * N

final activity = ln(2)/(2.63 * 365 * 24 * 3600) * 2.3*10^12

final activity = 19221.7 Bq

final activity = 19221.7 * 1/(37 *10^6) mCi

final activity = 0.000519 mCi