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  4. If No is the original mass of the substance of half-life period T1/2=5 yr, then the amount of substance left after 15 yr is

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Q. If No is the original mass of the substance of half-life period $T_{1/2}=5\, yr$, then the amount of substance left after $15\, yr$ is

Chhattisgarh PMTChhattisgarh PMT 2006

Solution:

$T_{1 / 2}=5\, yr,\, t=15\, yr$
$\therefore $ Number of half-lives
$(n)=\frac{t}{T_{1 / 2}}=\frac{15}{5}=3$
The amount of substance left undecayed.
$N=N_{0}\left(\frac{1}{2}\right)^{n}$
$=N_{0}\left(\frac{1}{2}\right)^{3} =\frac{N_{0}}{8}$