Nuclei of a radioactive element are being produced at a constant rate

CHEMISTRY · Multi-part · US High School · Chemistry · Atomic Structure & Nuclear · Atomic Structure & Nuclear

Problem

Nuclei of a radioactive element

A

are being produced at a constant rate

\alpha

. The element

A

has a decay constant

\lambda

. At time

t = 0

, there are

N_0

nuclei of element

A

. (1) Calculate the number of nuclei (

N

) of

A

at any time

t

. (2) If

\alpha = 2\lambda N_0

, calculate the number of nuclei of

A

after one half-life of

A

and also the limiting value of

N

t \to \infty