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  1. Home
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  3. /Periodic Table & Element Calculators
  4. /Isotope Distribution Calculator

Isotope Distribution Calculator

Calculator

Results

Heavy Isotope Abundance Used

1

%

Average Atomic Mass

36.966

amu

Average Molecular Mass

73.932

amu

Isotope Mass Spacing

1.997

amu

Probability All Light

0

%

Probability Exactly 1 Heavy

0

%

Probability Exactly 2 Heavy

100

%

Probability All Heavy

100

%

Probability Mixed Isotopes

0

%

Mass with 0 Heavy Atoms

69.938

amu

Mass with 1 Heavy Atom

71.935

amu

Mass with 2 Heavy Atoms

73.932

amu

Results

Heavy Isotope Abundance Used

1

%

Average Atomic Mass

36.966

amu

Average Molecular Mass

73.932

amu

Isotope Mass Spacing

1.997

amu

Probability All Light

0

%

Probability Exactly 1 Heavy

0

%

Probability Exactly 2 Heavy

100

%

Probability All Heavy

100

%

Probability Mixed Isotopes

0

%

Mass with 0 Heavy Atoms

69.938

amu

Mass with 1 Heavy Atom

71.935

amu

Mass with 2 Heavy Atoms

73.932

amu

The Isotope Distribution Calculator analyzes the isotopic pattern of molecules containing elements with two naturally occurring isotopes. When a molecule contains multiple atoms of a polyisotopic element, the resulting mass spectrum shows a characteristic isotope distribution pattern governed by binomial statistics. This pattern is crucial for mass spectrometry interpretation, where the isotope envelope helps identify molecular composition and confirm chemical formulas. For example, a molecule containing two chlorine atoms (Cl2) shows peaks at masses M, M+2, and M+4, reflecting the combinations of Cl-35 and Cl-37 isotopes. This calculator determines the average mass, probabilities of different isotopic compositions, and the most abundant molecular mass, providing essential information for interpreting experimental mass spectra and planning isotope labeling experiments.

Visual Analysis

How It Works

For a molecule containing n atoms of an element with two isotopes (light with abundance p and heavy with abundance q = 1-p), the isotope distribution follows the binomial distribution:

P(k heavy) = C(n,k) x p^(n-k) x q^k

Where C(n,k) is the binomial coefficient "n choose k" and k is the number of heavy isotope atoms (0, 1, 2, ..., n).

Key calculations:

  • P(all light): p^n - probability that all atoms are the light isotope
  • P(all heavy): q^n - probability that all atoms are the heavy isotope
  • P(mixed): 1 - p^n - q^n - probability of at least one of each isotope
  • Most abundant mass: For a dominant light isotope, this is typically mass_light x n

The average mass of the element is the weighted sum: M_avg = m_light x p + m_heavy x q. For molecules with multiple polyisotopic elements, the overall distribution is the convolution of individual element distributions.

Understanding Your Results

The probabilities show the expected intensity pattern in a mass spectrum. The most abundant peak (base peak in the isotope envelope) corresponds to the most probable isotopic composition. For elements with a dominant light isotope (like carbon, 98.9% C-12), the M peak (all light) is strongest. For elements with more balanced abundances (like bromine, ~50/50), the mixed peaks are strongest. The mass difference between isotopes determines the spacing between peaks in the mass spectrum. The probability of the all-heavy composition is important for understanding trace isotope peaks and for isotope dilution analysis.

Worked Examples

Example 1: Cl2 molecule

Inputs

abundance light75.76
mass light34.969
abundance heavy24.24
mass heavy36.966
num atoms2

Results

avg mass35.453
mass diff1.997
prob all light57.4
prob all heavy5.88
prob mixed36.72
mol mass most abundant69.938

Chlorine-35 (75.76%) and Chlorine-37 (24.24%) in Cl2 give a characteristic 3-peak pattern: 35Cl-35Cl at 69.94 amu (57.4%), 35Cl-37Cl at 71.93 amu (36.7%), and 37Cl-37Cl at 73.93 amu (5.9%). This approximately 9:6:1 ratio is a fingerprint for dichlorinated compounds in mass spectrometry.

Example 2: Br2 molecule

Inputs

abundance light50.69
mass light78.918
abundance heavy49.31
mass heavy80.916
num atoms2

Results

avg mass79.904
mass diff1.998
prob all light25.69
prob all heavy24.31
prob mixed50
mol mass most abundant157.836

Bromine's nearly equal isotope abundances (50.69% Br-79, 49.31% Br-81) create a distinctive 1:2:1 pattern in Br2: 79Br-79Br (25.7%), 79Br-81Br (50.0%), and 81Br-81Br (24.3%). This symmetric pattern is instantly recognizable in mass spectra and is diagnostic for brominated compounds.

Frequently Asked Questions

Isotope patterns serve as molecular fingerprints that help identify elemental composition. Each element has a unique isotope signature: chlorine produces peaks separated by 2 amu in a 3:1 ratio, bromine gives nearly equal peaks 2 amu apart, and sulfur shows a small M+2 peak. By matching observed patterns to calculated distributions, chemists can determine the number and type of polyisotopic elements in an unknown molecule.

In mass spectrometry, M refers to the monoisotopic peak (all atoms are the lightest isotope). M+1 is the peak one mass unit higher (one atom is a heavier isotope, typically C-13 or N-15). M+2 is two units higher (one atom of Cl-37, S-34, or Br-81, or two C-13 atoms). The M+1 and M+2 relative intensities help determine molecular formula.

More atoms create a broader isotope envelope with more peaks. For one Cl atom: 2 peaks (3:1). For two Cl atoms: 3 peaks (9:6:1). For three Cl atoms: 4 peaks (27:27:9:1). The envelope approaches a Gaussian distribution for large numbers of atoms, with the width proportional to the square root of n. This is why protein mass spectra show broad, smooth isotope envelopes.

Yes. Molecules with the same nominal mass but different formulas often have distinctly different isotope patterns. For example, C2H4O (MW 44) and CO2 (MW 44) have different M+1 intensities because C2H4O has more carbon atoms contributing to C-13 peaks. High-resolution mass spectrometry combined with isotope pattern analysis can unambiguously determine molecular formulas.

Isotope dilution adds a known amount of an enriched isotope to a sample to quantify the element or compound. By measuring the change in isotope ratio, the original amount can be calculated with very high accuracy. This technique, pioneered by Hevesy and Paneth, is considered a primary analytical method and is used for certified reference materials and forensic analysis.

Monoisotopic elements (F, Na, Al, P, Mn, Co, As, Au, etc.) contribute no isotope peaks because they have only one stable isotope. Molecules composed entirely of monoisotopic elements show a single peak with no isotope envelope. This simplifies mass spectral interpretation but provides less structural information than polyisotopic elements.

Sources & Methodology

Source: de Laeter, J.R. et al., Atomic Weights of the Elements, IUPAC Technical Report, Pure Appl. Chem. (2003). Reference: Gross, J.H., Mass Spectrometry: A Textbook, 3rd Edition, Springer (2017). Rockwood, A.L. et al., Isotopic Composition Techniques in Mass Spectrometry, Mass Spectrometry Reviews, 23, 507-548 (2004).
R

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