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
