A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t 1/2 . Show that after a time t t 1/2 , the number of active nuclei will become constant. Find the value of this constant.

Question

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t 1/2 . Show that after a time t >> t 1/2 , the number of active nuclei will become constant. Find the value of this constant.

Philoid · Accepted Answer

Given, rate of radioactive isotope production= R

Rate of decay= λN (∵ According to law of Radioacivity)

As activity decreases exponentially and after a time t >> t_1/2, the number of active nuclei will become constant and rate of decay will also become constant.

So, (dN/dt) _produce=(dN/dt) _decay=R

R= λN

⇒ N= =

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t1/2. Show that after a time t >> t1/2, the number of active nuclei will become constant. Find the value of this constant.

A radioactive isotope is being produced at a constant rate dN/dt = R in an experiment. The isotope has a half-life t_1/2. Show that after a time t >> t_1/2, the number of active nuclei will become constant. Find the value of this constant.