Determining naturally occuring isotopes of Bromine using mass spectrum information

Question

The element bromine has two naturally-occurring isotopes. A mass spectrum of molecular

Br2 shows three peaks with mass numbers of 158 u, 160 u, and 162 u. Use this information to

determine which isotopes of Br occur in nature.

Answer 1

Let us the atomic mass of the lighter isotope as x, and the atomic mass of the heavier isotope as y. For a diatomic molecule we would expect three major peaks:

x + x = 2x (both atoms are light)

x + y (one atom is light, the other is heavy)

y + y = 2y (both atoms are heavy)

Hence

2x = 158, so x = 79

2y = 162, so y = 81

Now, let us perform a sanity check. If the isotopes’ masses are 79 amu and 81 amu, then the molecule containing one of each isotopes will have a mass of 79 + 81 = 160 amu, which indeed the position of the middle peak.