Question

Mass numbers of two isotopes of an element differ by $2$ units ($A$ and $A+2$). Average atomic mass is $0.5$ more than the lower mass number. What could be the ratio of the percentage abundance two isotopes respectively?

Answer 1

Mass number of Isotope $1$=$A$

Mass number of Isotope $2$=$A+2$ {Both differ by two units}

Average atomic mass= $A+0.5$

Ration of percentage abundance of two isotopes= ?

Formula:- Let percentage abundance be $x$ & $100-x$ for $A$ and $A+2$ respectively.

Average atomic mass= $\frac{AtomicmassA\times x+AtomicmassA+2\times 100-x}{100}$

$\Rightarrow A+0.5=\frac{Ax+(A+2)(100-x)}{100}$

$\Rightarrow (A+0.5)100=Ax+A100-Ax+200-2x$

$\Rightarrow A100+50=Ax+A100-Ax+200-2x$

$\Rightarrow 50=200-2x$

$\Rightarrow 2x=200-50$

$\Rightarrow 2x=150$

$\therefore x=\frac{150}{2}=75$

$x=75$%

$100-x=25$%

Ratio of the percentage abundance of two isotopes=$75:25$