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  4. Tritium with a half-life of 12.5 years undergoing β -decay. What fraction of a sample of pure tritium will remain undecayed after 25 years?

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Q. Tritium with a half-life of 12.5 years undergoing $\beta $ -decay. What fraction of a sample of pure tritium will remain undecayed after 25 years?

NTA AbhyasNTA Abhyas 2020Atoms

Solution:

Given that, half-life of tritium
$t_{1 / 2}=12.5 \, $ years
$T=25 \, $ years
$\therefore $ Number of half-life, $n=\frac{T}{t_{1 / 2}}=\frac{25}{12.5}=2$
$\therefore $ Fraction of sample remain undecayed
$N=N_{0}\left(\frac{1}{2}\right)^{n},$ where, $N_{0}=$ initial sample
$=N_{0}\left(\frac{1}{2}\right)^{2}=\frac{N_{0}}{4}$