Physics

Problem

The decay constant of a radioactive species is

\lambda

for the process in which a parent element showing formation of a daughter element. After time

t

P

atoms of parent element are left and

D

atoms of daughter elements are formed. If

t_{1/2}

is half life then which expression correctly represents decay of parent element: a.

t = \frac{t_{1/2}}{0.693} \ln \left(1 + \frac{D}{P}\right)

t = \frac{t_{1/2}}{0.693} \ln \left(1 - \frac{D}{P}\right)

t = \frac{t_{1/2}}{0.693} \ln \left(\frac{D}{P}\right)

t = \frac{t_{1/2}}{0.693} \ln \left(\frac{P}{D}\right)