#### Question

Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.

#### Solution

Let the number of atoms present at t = 0 be N_{0}.

Let N be the number of radio-active isotopes present at time t.

Then,

N = N_{0}e^{−λt}

Here, `lambda` = Disintegration constant

∴ Number of radioactive isotopes decayed = `N_0 - N = N_0 - N_0e^(-lambdat)`

= `N_0(1-e^(-lambdat))` ...(1)

Rate of decay (R) is given by

`R = lambdaN_0` ...(2)

Substituting the value of `N_0` from equation (2) to equation (1), we get

`N = N_0(1-e^(-lambdat))`

= `R/lambda (1 - e^(-lambdat))`

Is there an error in this question or solution?

Solution Consider the Situation of the Previous Problem. Suppose the Production of the Radioactive Isotope Starts at T = 0. Find the Number of Active Nuclei at Time T. Concept: Radioactivity - Law of Radioactive Decay.