Question

Gallium is composed of two naturally occurring isotopes: Ga−69 (60.108%) and Ga−71. The ratio of the masses of the two isotopes is 1.0290. What is the mass of Ga-69?

Answer 1

Since there are only 2 isotopes of Gallium the abundance are:

Ga 69 = 0.6018

Ga 71 = 1 - 0.6018 = 0.3982

Let´s say :

Ga 69 = x

Ga 71 = y

x and y are the molecular weight (or a.m.u.) of the elements, please note that we have 2 unknown values therefore we will need 2 equations.

The ratio would be

$\frac{y}{x} = 1.029$ this would be equation 1

If we arrange it

x = 1.029 y

Equation 2 would be the average molecular weight of gallium according to the isotopes.

Average molecular weight of gallium = 69.723 a.m.u.

This is the result of the molecular weight of each isotope according to the abundance so:

69.723 = 0.6018 x + 0.3982 y ....... This is equation 2

Now we need to change the "x" for the one we got from equation 1:

69.723 = 0.6018 x + 0.3982 (1.029 x)

69.723 = 0.6018 x + 0.4097 x

69.723 = 1.0115 x

x = 69.723 / 1.0115 = 68.93 a.m.u

y = 68.93 * 1.029 = 70.93 a.m.u.

Mass of gallium 69 = 68.93 a.m.u.