There are 4?2 x 10^6 radioactive nuclei in a given radioactive sample. If the half life of the sample is 20 s, how many nuclei will decay in 10 s?

Dear Student,

Please find below the solution to the asked query:

According to the law of radioactivity,

$N = N_0 e^{-\lambda t}$
Where,
N = number of nuclei present at any time instant t,
N₀ = number of nuclei present at time t = 0 sec,
λ = is disintegration constant.

Given that N₀ = 4.2 x 10⁶ nuclei. Half life of the sample is $T_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} = 20 sec$. So, the disintegration constant is,

$\lambda = \frac{\ln \left(2\right)}{T_{{\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}}=\frac{\ln \left(2\right)}{20}$
So, after t = 10 sec, the number of nuclei remain is,


So number of nuclei decay
No -N  = 1.23 x10⁶ Nuclei
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