The decay constant of a radioactive species is for the process in which a parent…

PHYSICS · Single correct · A Level · Physics · Nuclear physics · Nuclear 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: (1)

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

(2)

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

(3)

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

(4)

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