Question

An element X exists in two isotopic forms with atomic masses 11 u and 13 u respectively with average atomic mass of 12.5 u. The percentage abundance of the isotope with atomic mass 11 is

Answer 1

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } GiveN:-}}}}}$

• A element X exists in two isotopic forms.
• Atomic mass of one isotope is 11u.
• Atomic mass of second isotope is 13u.
• Average Atomic mass is 12.5u .

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } To\:FinD:-}}}}}$

• The percentage of abundance of isotope with atomic mass 11.

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } FormulA\:UseD:-}}}}}$

We can calculate Average atomic mass as ,

$\large\pink{\underline{\boxed{\purple{\tt{\dag Atomic\:mass_{average}=\dfrac{(Abundance\%)\times(Mass_{X_1})+(Abundance\%)\times(Mass_{X_2})}{100} }}}}}$

$\large{\underline{\underline{\red{\tt{\purple{\leadsto } AnsweR:-}}}}}$

Let the average atomic mass of first isotope be x% , then the percentage of second isotope will be (100-x)%.

Now , Let the first Isotope be denoted by $\sf X_1$ with mass 11u and second by $\sf X_2$ with mass 13u.

Now , put the respective values in above formula stated :

$\tt:\implies Atomic\:mass_{avg.}=\dfrac{ (Abundance\%)\times(Mass_{X_1})+(Abundance\%)\times(Mass_{X_2})}{100}$

$\tt:\implies 12.5u=\dfrac{x\times11u+(100-x)\times13u}{100}$

$\tt:\implies 12.5\times100=11x+1300-13x$

$\tt:\implies1250=-2x+1300$

$\tt:\implies 2x = 1300-1250$

$\tt:\implies2x=50$

$\tt:\implies x=\dfrac{50}{2}$

$\underline{\boxed{\red{\tt\longmapsto \:\:x\:\:=\:\:25\%}}}$

$\orange{\boxed{\green{\bf \dag Hence\: percentage\:of\:X_1\:is\:25\%.}}}$