Copper is listed on the periodic table as having a relative atomic mass of 63.55. Reference books indicate two isotopes of copper, with relative masses of 62.93 and 64.93. What is the percent abundance of each isotope?

Question

Serenity Allen · Accepted Answer

#69%# for the isotope that weighs 62.93 u and #31%# for the isotope that weighs 64.93 u. You can approach this problem by using a single equation; let's say the first isotope contributes to the relative atomic mass by a fraction #x# (#x<1#). SInce there are only 2 isotopes to consider, the fraction the other isotope contributes with will automatically be #1-x#. Let's construct the formula. #x * 62.93u + (1-x) * 64.93u = 63.55u# Solving this for #x# will produce #64.93u - 63.55u = 2x -> x = 1.38/2 = 0.69# To obtain the results as a percentage, multiply these fractions (0.69 and 1-0.69 = 0.31) by 100%. This will yield #69%# for  the isotpe that weighs 62.93u and
#31%# for the one that weighs 64.93u.

Xavier Avery · Answer

undefined Using their respective atomic masses and the given average relative atomic mass of copper (63.55), the percent abundance of each copper isotope can be determined. Let's denote the percent abundance of the isotope with a relative atomic mass of 62.93 as x, and the percent abundance of the isotope with a relative atomic mass of 64.93 as (100 - x). Applying the weighted average formula: $$62.93x + 6493 - 64.93x = 63.55$$
$$-2x + 6493 = 63.55$$
$$-2x = -6429.45$$
$$x = 3214.725$$

This means that the isotope with a relative atomic mass of 62.93 is approximately 32.15%, and the isotope with a relative atomic mass of 64.93 is approximately 67.85%.