Isotopes: Finding the mass of a missing isotope

Another interesting variation of an isotopes question is where you need to determine the mass number of a missing isotope.

This is another type of question where algebra is needed.

Question: A sample of boron contains 2 isotopes and has an Ar of 10.8. The lighter isotope has a mass number of 10 and abundance of 20%. Determine the mass number and abundance of the heavier isotope.

Answer

We start by filling in the table. We have two unknowns – the mass number and abundance of the heavier isotope. However, the abundance of the heavier isotope is obviously 80% as the abundances must add up to 100%.

Mass10m
Abundance20%80%

We can then write out the Ar equation and solve for m:

[(10 x 20%) + (m x 80%)]/100% = 10.8

(10 x 20%) + (m x 80%) = 1080

200 + 80 m = 1080

80 m = 880 –> m = 11

i.e., the heavier isotope is 11B with an abundance of 80%