Isotope Pattern Calculator Formula

Understand the math behind the isotope pattern calculator. Each variable explained with a worked example.

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Formulas Used

M+1 Relative Intensity

mplus1 = (c_atoms * 1.1 + h_atoms * 0.015 + n_atoms * 0.37 + o_atoms * 0.04 + s_atoms * 0.8)

M+2 Relative Intensity

mplus2 = pow(c_atoms * 1.1 + h_atoms * 0.015 + n_atoms * 0.37 + o_atoms * 0.04 + s_atoms * 0.8, 2) / 200 + o_atoms * 0.20 + s_atoms * 4.4

Variables

VariableDescriptionDefault
c_atomsNumber of Carbons10
h_atomsNumber of Hydrogens14
n_atomsNumber of Nitrogens2
o_atomsNumber of Oxygens3
s_atomsNumber of Sulfurs0

How It Works

Isotope Pattern Estimation

The natural isotope distribution creates characteristic patterns in mass spectra. The M+1 and M+2 peaks relative to the monoisotopic (M) peak help identify molecular formulas.

Approximate Rules

M+1 contributions per atom: C = 1.1%, H = 0.015%, N = 0.37%, O = 0.04%, S = 0.8%

M+2 contributions: O = 0.20% each, S = 4.4% each, plus (M+1)²/200

These are approximations. Accurate patterns require full combinatorial calculation, especially for chlorine and bromine-containing compounds.

Worked Example

Estimate isotope pattern for C10H14N2O3.

c_atoms = 10h_atoms = 14n_atoms = 2o_atoms = 3s_atoms = 0
  1. 01M+1 = 10×1.1 + 14×0.015 + 2×0.37 + 3×0.04 = 11.0 + 0.21 + 0.74 + 0.12 = 12.07%
  2. 02M+2 = 12.07²/200 + 3×0.20 = 0.73 + 0.60 = 1.33%

Frequently Asked Questions

Why are isotope patterns useful?

Isotope patterns provide complementary information to exact mass. Two formulas with similar masses may have very different isotope patterns. Chlorine and bromine create distinctive doublet and triplet patterns.

How do Cl and Br affect isotope patterns?

Cl has 75.8% Cl-35 and 24.2% Cl-37 (M+2 = ~32% per Cl). Br has 50.7% Br-79 and 49.3% Br-81 (nearly equal M and M+2). These create unmistakable patterns even at low resolution.

When does this approximation break down?

For large molecules (proteins, polymers), the monoisotopic peak may not be the most abundant. For Cl/Br compounds, exact binomial calculations are needed. Use dedicated software for accurate predictions.

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