# How to Calculate Percent Abundances

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An isotope of an element is a variant in the nuclear makeup of the atom. Isotopes have different numbers of neutrons from atom to atom of the same element. The number of protons in the nucleus does not change from atom to atom. The mass number for every element is the number of protons and neutrons found in the nucleus. Because isotopes have a different number of neutrons, the mass number is not the same and is a method of identification of isotopes. The percent abundance of the isotopes is the relative percentage of a particular isotope. If the mass numbers of the isotopes are known and the element's periodic table average mass number is known, simple algebra can be used to calculate the percent abundance.

### Things You'll Need

• Periodic table of the elements
• Calculator
• Determine the element's average atomic mass number using the periodic table of the elements. This will be a number with several decimal places behind it. This value is the average mass number of all of the element's isotope mass numbers. For instance, carbon has an average atomic mass number of 12.011.

• Determine the atomic mass numbers of the isotopes of an element. For instance carbon 12 has a mass number of 12.000 and carbon 13 has a mass number of 13.034.

• Determine the percent abundance of two isotopes using an algebraic formula. For instance, (c12 mass)(x) + (c13 mass)(1 - x) = average mass number. This formula is 12.000 (x) + 13.034 (1 - x) = 12.011 where x represents the fraction abundance. This formula distributes to 12.000x + 13.034 - 13.034x = 12.011, reduces to -1.034x = -1.023 and has x equal to 0.9894. So, the c12 percent abundance is 98.94 percent (0.9894 x 100) and the percent abundance of c13 is 1 - x or 1.06 percent.

## References

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