Gallium arsenide, GaAs, has gained widespread use in semiconductor devices that convert light and electrical signals in fiber-optic communications systems. Gallium consists of 60.% 69Ga and 40.% 71Ga. Arsenic has only one naturally occurring isotope, 75As. Gallium arsenide is a polymeric material, but its mass spectrum shows fragments with the formulas GaAs and Ga2As2. What would the distribution of peaks look like for these two fragments?

Five peaks

Explanation:

GaAs would show two peaks:

Ga-69 + As-75 = 144

Ga-71 + As-75 = 146

Their intensities are in the ratio 60 : 40 = 100:67.

Ga₂S₂ would show three peaks:

Ga-69 + Ga-69 + 2As-75 = (Ga-69) ₂ (As-75) ₂ = 288

Ga-69 + Ga-71 + 2As-75 = (Ga-69) (Ga-71 (As-75) ₂ = 290

Ga-71 + Ga-71 + 2As-75 = (Ga-71) ₂ (As-75) ₂ = 292

Their relative intensities are in the ratio

(60 + 40) ² = 60² : 2*60*40 : 40² = 3600 : 4800 : 1600 = 75 : 100 : 33

A spectrum of a mixture of GaAs and Ga₂As₂ would show five peaks:

Two at m/e 144 and 146 with intensity ratios 100: 67 and

Three at m/e 288, 290, and 292 with intensity ratios 75:100 : 33.

We cannot predict the absolute sizes of the peaks because we do not know the relative amounts of GaAs and GaAs₂.