Question

Boron occurs in nature in the form of two isotopes having atomic mass 10 and 11. Calculate the percentage abundances of two isotopes respectively in a sample having atomic mass 10.80 .

Answer 1

Hint: An attempt to this question can be made by understanding the term isotopes. Try to understand the differentiating factor in isotopes. The percentage abundance of the two isotopes can be determined by the formula given below:
Average atomic mass = ${\displaystyle \frac{\text{y x 10 + (100 - y})\text{ x 11}}{100}}$
Where, y is the percentage of mass of one of the isotopes.

Complete step-by-step solution:
Isotopes are variants of a particular chemical element which differ in only the number of neutrons present in the nucleus. Due to this their mass number also varies.
It is given to us that the average atomic mass of boron is 10.80. The mass number of the two isotopes of boron are 10 and 11 respectively.
We will now substitute the value of average atomic mass in the formula given above to obtain the value of y.
10.80 = ${\displaystyle \frac{\text{y x 10 + (100 - y})\text{ x 11}}{100}}$
1080 = 10y + 1100 - 11y
y = 20.
Thus 100 - y = 80.
From the above statements we can conclude that the percentage abundances of the two isotopes of boron respectively in a sample having atomic mass 10.80 is 20 and 80.

Therefore, the correct answer is option (C).

Note: It is important to know that the percentage of boron isotope having mass number 10 is taken as 20%. This is because the average atomic mass is 10.80 i.e. towards 11. Thus the isotope having mass number 11 has a greater contribution towards the average mass number.