# 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?

Dec 22, 2014

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 set up the equation

$x \cdot 62.93 u + \left(1 - x\right) \cdot 64.93 u = 63.55 u$

Solving this for $x$ will produce

$64.93 u - 63.55 u = 2 x \to x = \frac{1.38}{2} = 0.69$

Multiplying these fractions (0.69 and 1 - 0.69 = 0.31) by 100% percent to get the results as a percentage will give

69% for the isotpe that weighs 62.93u and
31% for the one that weighs 64.93u.