JEE Advance - Chemistry (1978 - No. 3)

Let, percentage of isotope with atomic weight $$10.01 = x$$

and percentage of isotope with atomic weight $$11.01 = 100 - x$$

We know, average atomic weight formula,

$${A_{avg}} = {{\sum {\left( {\% \,\mathrm{of}\,{I_i} \times \mathrm{Atomic\,Weight}} \right)} } \over {\sum {\left( {\% \,\mathrm{of}\,{I_i}} \right)} }}$$

Here $${I_i}$$ = i th isotope of an element.

Here given,

$${A_{avg}} = 10.81$$

$$\therefore$$ $$10.81 = {{10.01 \times x + 11.01 \times (100 - x)} \over {x + 100 - x}}$$

$$ \Rightarrow 10.81 = {{10.01x + 11.01(100 - x)} \over {100}}$$

$$ \Rightarrow 1081 = 10.01x + 1101 - 11.01x$$

$$ \Rightarrow x = 1101 - 1081$$

$$ \Rightarrow x = 20$$

$$\therefore$$ Isotope with weight 10.01 present = 20% and isotope with weight 11.01 present = 80%