Question

if we start with 8000 atoms of radium-226, how much would remain after 3,200 years?

Answer 1

Half life of Radium-226 is 1600 years.

Radioactive decay follows first order kinetics.

$\lambda =ln2/t_{1/2}=0.693/t_{1/2}$

$N_t=N_oe^{- \lambda t}$

Initial neclei are given as 8000.

$N_t=8000e^{- ln2*3200/1600}$

$=8000 e^{-2ln2}=2000$

Thus, 2000 atoms remain after 3200 years.