Question

Please help me solve this question

1. After 38 days, all that is left of a 50g sample of an isotope is 0.0488 g. Which isotope is this?
(graph 1)

Answer 1

The radioactive decay follows first order kinetics

The integrated rate law expression for first order rate is

ln(A / At) = kt

Where A= initial concentration

At=concentration at time "t"

t = time

K= rate constant

ln(50 / 0.0488) = k X 38

Therefore

K = 0.1824 day-1

The relation between rate constant and half life is

So half life = 0.693 / 0.1824 = 3.8 days

So isotope must be Radon-222