Kinetics please help quick?

Question

The first order decay of a radionuclide was observed. The initial activity was 0.00658 disintegrations per second per gram and after 317 seconds, the activity was 0.00213 disintegrations per second per gram. What is the half-life, in seconds, of the radionuclide?

Answer 1

The decay formula is

E = E0*e^-t/tc

Find tc from the given values at t = 317:

0.00213 = 0.00658*e^-317/tc

ln(0.00213) = ln(0.00658) - 317/tc

solve for the time constant tc:

tc = 317/[ln(0.00658) - ln(0.00213)]

tc = 281 sec

The half life th is given by

E/2 = E*e^-th/tc

ln(0.5) = -th/tc

th = tc*ln(2) = 281*ln(2)

th = 195 sec