Question

Gallium has two naturally occurring isotopes. The mass of gallium-69 is 68.9256 amu and it is 60.108% abundant. The mass of gallium-71 is 70.9247 amu and it is 39.892% abundant. What is the atomic mass of gallium?

Answer 1

`"M"_r (Ga) = 69.7231 " to 4 decimal places"`.

Explanation:

To find the average atomic mass (`"A"_r`) of an element, given the percentage rarities of its isotopes, simply multiply each isotope's `"A"_r` by its percentage that is expressed as a decimal and total the results. We can carry this out in a single line of working:

`"M"_r ("Ga") = (68.9256 * 0.60108) + (70.9247 * 0.39892)`
`"M"_r ("Ga") = 69.7231 " to 4 decimal places"`

Similarly, you could input the percentages normally and then divide by `100`:

`"M"_r ("Ga") = ((68.9256 * 60.108)+(70.9247 * 39.892))/100`

`"M"_r ("Ga") = 69.7231 " to 4 decimal places"`

Notice that the answers are the same. Also observe that the answer is closer to 69 than it is to 71, which makes sense since gallium-69 makes up a greater proportion of gallium in the universe (`~60%`) than gallium-71 does (`~30%`).