Isotope Pattern Calculator Formula

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

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%

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