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?

Question

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? (A) One half (B) One fourth (C) One third (D) Three fourth

Tardigrade Admin · Accepted Answer

Given that, half-life of tritium t1 / 2=12.5 years T=25 years ∴ Number of half-life, n=(T/t1 / 2)=(25/12.5)=2 ∴ Fraction of sample remain undecayed N=N0((1/2))n, where, N0= initial sample =N0((1/2))2=(N0/4)

Q. 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?

One half

One fourth

One third

Three fourth

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

Q. 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?