A fictitious element X is composed of 20.0 percent of the isotope , 40.0 percent of the isotope , and 40.0 percent of the isotope . Estimate the atomic mass of element X.
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First of all, atomic mass is the weighted average of the masses of all isotopes of an element. So, if you have an element with 2 isotopes, each of equal abundance, the atomic mass will be smack dab in the center.
Here, you don't have equal abundance. Ignore the algebra... what do you expect the atomic mass to be? First, it will be somewhere between 55 and 57 amu, right? Will it be closer to 55, 56, or 57? Since the most abundant isotope is the 57 isotope, you might expect the final atomic mass to be closest to 57 (somewhat less, since the average will be pulled down by the 55 and 56 isotopes).
Well, the equation that takes into account the abundances is nothing more than the equation for taking averages. If you take 5 tests and score 85, 85, 89, 89, and 97, what was your average score? The total score was 85*2 + 89*2 + 97*1 = 445. To get the average, you divide by 5... the average was 445/5 = 89.
Same for elements. Assume here that you have 100 atoms of the element. The percentage tells you that you have 10 atoms of the 55 isotope, 20 of the 56, and 70 of the 57.
10*55 + 20*56 + 70*57 = 5,660. To get the average (a.k.a. the atomic mass), just divide by the total number of atoms (100).
Atomic mass = 5660/100 = 56.6
Just like the prediction, the atomic mass is within 55-57 and closest to the isotope of highest abundance (57).
stephen j · 7 years ago