A hypothetical element has two isotopes: 79.18% have a mass of 139.9 amu, while the rest are 164.8 amu. What is the atomic mass of this element?

Question

A hypothetical element has two isotopes: 79.18% have a mass of 139.9 amu, while the rest are 164.8 amu. What is the atomic mass of this element?

Answer 1

The mass listed for each element on the period table is the weighted average of the mass of all of the isotopes of that element. For this element, there are only two isotopes.

To find the weighted average we can use this calculation:

(% prevalence isotope 1) * (weight isotope 1) + (% prevalence isotope 2) * (weight isotope 2)....

for this element,

mass = (.7918)*(139.9) + (1-.7918)*(164.8) = 145.084

Make sure to account for significant figures, which would make this answer 145.1 amu.

Answer 2

The idea here is that we're going to take a weighted mean of the two different isotopes. When we say, for example, that the atomic mass of carbon is 12.011 amu, we don't mean that any particular atom has that weight -- they're all either 12 or 13 amu individually. However, they are 12.011 on average.

79.18% have a mass of 139.9 and the rest have a mass of 164.8. The rest, in this case, is 100% - 79.18% = 20.88%. We divide the percentage by 100 to get our weights. So:

0.7918 * 139.9 amu + 0.2088 * 164.8 amu = 145.2 amu

https://en.wikipedia.org/wiki/Weighted_arithmetic_mean