An element has two isotopes with atomic masses $(A-1)$ and $(A+3)$ respectively. The average atomic mass is $A$. Calculate the mole percentage of the heavier isotope.

The correct option is B $25$%
mass of two isotype are $(A-1)$ and $(A+3)$

Let the $\%$ of isotypes which is lighten $=x$

$\therefore \%$ of isotopes which is heavier $=(100-x)$

Now

$ATQ$ Average mass of element $=A$

Average mass of element$=\frac{\stackrel{n}{\sum _i}\left(\%\text{Abundance of the isotope}\right)A_i\times A_i}{100}$

$\therefore A=\frac{x(A-1)}{100}+\frac{(100-x)(A+3)}{100}$

$\Rightarrow Ax-x+100A+300-Ax-3x=100A$

$4x=300$

$x=75\%$

$\therefore \%$ of heavier isotype $=(100-75)\%$

$=25\%$