Naturally occurring gallium consists of two isotopes. One of those isotopes is 71Ga with an isotopic mass of 70.9247050 amu and an abundance of 39.892%. What is the mass number of the other isotope?

The answer is 69.

Relative atomic mass of an element is a sum of the products of each isotopic mass and its abundance. We first need to calculate the isotopic mass of the second isotope to find out its mass number.

So,

- the isotopic mass of the first isotope: Ar1 = 70.9247050 amu

- the abundance of the first isotope: a1 = 39.892% = 0.39892

- the abundance of the second isotope a2 = 100% - a1 = 100% - 39.892% = 60.108% = 0.60108

- the isotopic mass of the second isotope is unknown: Ar2 = ?

Thus, using the formula:

Ar (Ga) = Ar1 * a1 + Ar2 * a2

69.723 = 70.9247050 * 0.39892 + Ar2 * 0.60108

69.723 = 28.2932833186 + 0.60108 Ar2

0.60108 Ar2 = 69.723 - 29.2832833186 = 41.4297166814

Ar2 = 41.4297166814 / 0.60108 = 68.92546197078592 amu ≈ 69 amu

Since the isotopic mass of the second isotope is ≈ 69 amu, the mass number of the isotope is 69.