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To determine the percent abundance of an isotope, you combine the element’s average atomic mass from the periodic table with a simple algebraic equation.
Relative abundance is the percentage of a specific isotope found in nature. The atomic mass listed for an element on the periodic table is a weighted average of all its naturally occurring isotopes.
Isotopes share the same number of protons but differ in neutron count. For example, nitrogen‑14 has 7 neutrons, whereas nitrogen‑15 has 8 neutrons; both are nitrogen but distinct isotopes.
Typical problems ask you to compute either the relative abundance of a particular isotope or the mass of that isotope given the element’s average atomic mass.
Locate the element’s average atomic mass on the periodic table. For nitrogen, this value is 14.007 amu.
Use the standard formula:
(M₁)(x) + (M₂)(1 – x) = M(E)
M₁ = mass of isotope 1x = relative abundance (as a decimal) of isotope 1M₂ = mass of isotope 2M(E) = element’s average atomic massExample: Nitrogen‑14 (14.003 amu) and nitrogen‑15 (15.000 amu). Plugging into the formula gives
14.003 x + 15.000 (1 – x) = 14.007
Apply algebraic steps:
• Distribute: 14.003 x + 15.000 – 15.000 x = 14.007
• Combine like terms: –0.997 x = –0.993
• Divide: x = 0.996
Multiply the decimal by 100 to express as a percentage.
0.996 × 100 = 99.6 %(1 – 0.996) × 100 = 0.4 %When a mass spectrum is provided, relative abundances are often shown as a vertical bar chart. Although the total can appear to exceed 100 %, the bars represent relative percentages. For a nitrogen pattern, the spectrum might display 100 for nitrogen‑14 and 0.37 for nitrogen‑15.
Normalize these values:
nitrogen‑14 = 100 / (100 + 0.37) ≈ 0.996 → 99.6 %
nitrogen‑15 = 0.37 / (100 + 0.37) ≈ 0.004 → 0.4 %
By following these steps, you can reliably calculate the percent abundance of any isotope.
