Question

If a radioactive compound has nuclei N₀ and decay constant λ, Find the total number of nuclei after time t.
1. \(N_0 e^{+λ t}\)
2. \(N_0 e^{-λ t}\)
3. \(N_0 e^{-λ \over t}\)
4. \(N_0 e^{λ \over t}\)

Answer 1

Correct Answer - Option 2 : \(N_0 e^{-λ t}\)

CONCEPT:

• As per radioactive decay law, the total number of nuclei of radioactive compounds after radioactive decay in the sample is given by the given equation:

\(N=N_0 e^{-λ t}\)

where N is the number of nuclei of radioactive compounds after radioactive decay, N0 is the number of nuclei of radioactive compounds initially, λ is the decay constant and t is the time of radioactive decay.​

EXPLANATION:

Given that initially, the number of atoms is N0 and decay constant λ.

So the total number of nuclei, the radioactive compound will have after time 't'

\(N=N_0 e^{-λ t}\)

So the correct answer is option 2.