# How to Find Fractional Abundance of an Isotope

by Matthew Perdue, Demand Media

Isotopes of a particular element are atoms that contain the same number of protons and electrons but have a different number of neutrons. Due to the added neutrons, these atoms have a different atomic mass. This variation in mass, however, does not affect the chemical reactivity of the isotopes, as they will chemically react like their respective element. The fractional abundance, normally represented as a percentage, of each isotope of a given element can be calculated based on the average atomic mass of the element and the individual atomic mass of each isotope.

Identify the average atomic mass of the element and the individual mass of each isotope of the respective element. This information is readily available for almost all elements. For example, carbon only has two stable, naturally occurring isotopes --- carbon-12 and carbon-13. According to the Scientific Instrument Services, carbon-12 has a mass of 12.0000 and carbon-13 has a mass of 13.0033. The average atomic mass of carbon is identified in the periodic table as 12.0110.

Enter these weights into the formula (b)x + (1-x)(c) = a, where "a" is the average atomic mass of the element, "b" is the mass of the first isotope, "c" is the mass of the second isotope, and "x" represents the unknown abundance. For carbon, the formula would be written as: (13.0033)x + (1-x)(12.0000) = 12.0110

Solve for the x variable. For example: 13.0033x + 12.0000-12.0000x = 12.0110 1.0033x = 0.0110 x = 0.011

Identify this value as the fractional abundance, or multiply this value by 100 and identify it as the percent abundance of the first isotope in the equation. The abundance of carbon-13 would then be 0.011 or 1.1 percent.

Subtract x from 1 to determine the fractional abundance of the second isotope, and multiply the value by 100 to identify the percent abundance. The abundance of carbon-12 would then be 0.989 or 98.9 percent. 1 -- 0.011 = 0.989 0.989 * 100 = 98.9 percent

#### Things You Will Need

• Periodic table of elements
• Calculator