Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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# 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. - Physics

#### 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 N0.
Let N be the number of radio-active isotopes present at time t.
Then,
N = N0e−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))

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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.
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