Question

Gallium arsenide $\mathbf{GaAs}$has gained widespread use in semiconductor devices that interconvert light and electrical signals in fibre-optic communications systems. Gallium consists of 60%${}^{\mathbf{69}}\mathbf{Ga}$and 40%${}^{\mathbf{71}}\mathbf{Ga}$. Arsenic has only one naturally occurring isotope. . Gallium arsenide is a polymeric material, but its mass spectrum shows fragments with formulas $\mathbf{GaAs}$and ${\mathbf{Ga}}_{\mathbf{2}}{\mathbf{As}}_{\mathbf{2}}$. What would the distribution of peaks look like for these two fragments?

Short answer

The possibilities of the isotope

	${}^{69}Ga{}^{75}As$	${}^{71}Ga{}^{75}As$
Mass (amu)	$144$	$146$
Relative abundance	$60\%$	$40\%$

The distribution of peaks for the two fragments:

Mass( amu)	Relative abundance
$144$	$60\%$
$146$	$40\%$

Step-by-step solution

Definition of formula

The actual formula mass of each molecule depends on the actual mass of each isotope in the formula. Because of the existence of different isotopes, the distribution of peaks for a compound depends on the possibility of each combination of all isotopes.

 Calculation of relative abundance

For ${}^{69}G{a}_2{}^{75}A{s}_2$

$$\begin{gathered} 0.60\times 0.60=0.36 \\ 0.36\times 100\%=36\% \end{gathered}$$

For${}^{69}G{a}_2{}^{71}Ga{}^{75}A{s}_2$

$$\begin{gathered} 0.60\times 0.40=0.24 \\ 0.24\times 100\%=24\% \end{gathered}$$

For ${}^{69}G{a}_2{}^{71}Ga{}^{75}A{s}_2$

$$\begin{gathered} 0.40\times 0.60=0.24 \\ 0.24\times 100\%=24\% \end{gathered}$$

For${}^{69}G{a}_2{}^{75}A{s}_2$

$$\begin{gathered} 0.40\times 0.40=0.16 \\ 0.16\times 100\%=16\% \end{gathered}$$

Distribution of peaks

Mass(amu)	Relative abundance
$288$	$36\%$
$290$	$(24+24)=48\%$
$292$	$16\%$