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Q.
The mass of an object changes from $0.2\, g$ to $0.025 \,g$ in $1500$ years. The half life of the object is:
ManipalManipal 2004
Solution:
Given that
Initial value $N_{o}=0.2\, gm$.
Final value $(N)=0.025 \,gm$
Time decay $(T)=1500$ yrs.
By using :
$\frac{N}{N_{o}} =\left(\frac{1}{2}\right)^{n} $
$\frac{0.025}{0.2} =\left(\frac{1}{2}\right)^{n} $
or $ \frac{1}{8} =\left(\frac{1}{2}\right)^{n} $
or $\left(\frac{1}{2}\right)^{3} =\left(\frac{1}{2}\right)^{n} $
or $ n=3 $
Now by using
$t_{1 / 2} =\frac{T}{n}=\frac{1500}{3} $
$=500 \,yrs$