This problem is from chemistry.

Question

A element is composed of 2 isotopes: Isotope 1 has a mass of 294.3 amu and isotope 2 has a mass of 297.0 amu. If isotope 1 has a relative abundances of 34.6% then what is the atomic mass of the element?

Answer 1

Thankfully, this doesn't require much math. Recall that the way we (and IUPAC) determine an element's atomic mass is by a weighted average of the isotopes which occur in nature. This means we simply take the relative abundance of each isotope, convert it to decimal form, then multiply each abundance by their respective atomic weight, then sum them. The formula for a weighted average is ∑(X_i • M_i), where M_i is the atomic mass of isotope i, and X_i is the relative abundace of isotope i, in decimal form. So, here, we get:

(294.3 • 0.346)+(297.0 • (1-0.346)), since the abundance of isotope 2 is just 100% subtract the abundance of isotope 1. This equation gives us 296.0658, which, since we have 4 significant figures on our atomic masses, should be recorded as 296.1 amu.