Question

An element exists in the form of two isotopes with mass numbers x and x+ 2. If the percentage abundance of these isotopes is 75.77% and 24.23%, then what is the average atomic mass of the element?

• A. x+0.5
• B. x+ 0.25
• C. x+ 0.75
• D. x+1

Answer 1

The correct option is A

x+0.5

Isotopes- They are the atoms of an element that have the same number of protons but a different number of neutrons.

The average atomic mass of any element-It is defined as the sum of the atomic masses of each isotope multiplied by their natural abundance.

$\mathrm{Average}\mathrm{atomic}\mathrm{mass}=\sum _{\mathrm{i}=1}^{\mathrm{i}=\mathrm{i}}(\mathrm{Atomic}\mathrm{mass}\mathrm{of}\mathrm{isotope}\mathrm{i}\times \mathrm{Abundance}\mathrm{of}\mathrm{isotop}e\mathrm{i})$

The explanation for the correct option: (a)

1. There are two isotopes of the given element with mass numbers (x) and (x+2).
2. The abundance of isotope 1 is 75.77 % (= 0.7577) and the abundance of isotope 2 is 24.23 % (0.2323).
3. Thus, their average atomic mass is calculated as-

$$\begin{gathered} \mathrm{Average}\mathrm{atomic}\mathrm{mass}=\mathrm{x}(0.7577)+(\mathrm{x}+2)(0.2423) \\ =0.7577\mathrm{x}+0.2423\mathrm{x}+0.4846 \\ =1\mathrm{x}+0.4846 \\ \therefore \mathrm{Average}\mathrm{atomic}\mathrm{mass}=\mathrm{x}+0.5(\mathrm{after}\mathrm{approximation}) \end{gathered}$$

The correct option is (a).