How to Calculate Atomic Mass

Atomic Mass Calculator

Isotope 1

Isotope 2

Isotope 3 (Optional)

function calculateAtomicMass() { var isotopes = []; var totalAbundance = 0; // Isotope 1 var mass1 = parseFloat(document.getElementById('isotope1Mass').value); var abundance1 = parseFloat(document.getElementById('isotope1Abundance').value); if (!isNaN(mass1) && !isNaN(abundance1) && abundance1 > 0) { isotopes.push({ mass: mass1, abundance: abundance1 }); totalAbundance += abundance1; } else if (abundance1 < 0) { document.getElementById('atomicMassResult').innerHTML = 'Error: Abundance cannot be negative.'; return; } // Isotope 2 var mass2 = parseFloat(document.getElementById('isotope2Mass').value); var abundance2 = parseFloat(document.getElementById('isotope2Abundance').value); if (!isNaN(mass2) && !isNaN(abundance2) && abundance2 > 0) { isotopes.push({ mass: mass2, abundance: abundance2 }); totalAbundance += abundance2; } else if (abundance2 < 0) { document.getElementById('atomicMassResult').innerHTML = 'Error: Abundance cannot be negative.'; return; } // Isotope 3 var mass3 = parseFloat(document.getElementById('isotope3Mass').value); var abundance3 = parseFloat(document.getElementById('isotope3Abundance').value); if (!isNaN(mass3) && !isNaN(abundance3) && abundance3 > 0) { isotopes.push({ mass: mass3, abundance: abundance3 }); totalAbundance += abundance3; } else if (abundance3 < 0) { document.getElementById('atomicMassResult').innerHTML = 'Error: Abundance cannot be negative.'; return; } if (isotopes.length === 0) { document.getElementById('atomicMassResult').innerHTML = 'Please enter valid mass and abundance for at least one isotope.'; return; } // Check if total abundance is close to 100% if (Math.abs(totalAbundance – 100) > 0.1) { // Allow for slight floating point inaccuracies document.getElementById('atomicMassResult').innerHTML = 'Warning: Total abundance is ' + totalAbundance.toFixed(2) + '%. It should ideally be 100%.'; return; } var weightedSum = 0; for (var i = 0; i < isotopes.length; i++) { weightedSum += isotopes[i].mass * (isotopes[i].abundance / 100); } document.getElementById('atomicMassResult').innerHTML = 'Calculated Atomic Mass: ' + weightedSum.toFixed(4) + ' amu'; }

Understanding Atomic Mass

The atomic mass of an element is a weighted average of the masses of its naturally occurring isotopes. Unlike the mass number (which is simply the total number of protons and neutrons in a specific isotope), atomic mass takes into account the relative abundance of each isotope found in nature.

What are Isotopes?

Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This difference in neutron count leads to different atomic masses for each isotope. For example, Carbon-12 and Carbon-14 are isotopes of carbon; both have 6 protons, but Carbon-12 has 6 neutrons while Carbon-14 has 8 neutrons.

Why a Weighted Average?

When you look at the periodic table, the atomic mass listed for an element isn't usually a whole number. This is because it reflects the average mass of all the isotopes of that element, weighted by their natural abundance. If an element has one isotope that is much more common than others, that isotope's mass will contribute more significantly to the element's overall atomic mass.

How to Calculate Atomic Mass

The formula for calculating atomic mass is straightforward:

Atomic Mass = (Isotope 1 Mass × Isotope 1 Abundance) + (Isotope 2 Mass × Isotope 2 Abundance) + …

Where:

• Isotope Mass: The exact atomic mass of a specific isotope, usually measured in atomic mass units (amu).
• Isotope Abundance: The relative percentage of that isotope found in nature, expressed as a decimal (e.g., 75% becomes 0.75).

Example: Chlorine (Cl)

Let's consider Chlorine, which has two major naturally occurring isotopes:

• Chlorine-35: Has an atomic mass of approximately 34.96885 amu and a natural abundance of 75.77%.
• Chlorine-37: Has an atomic mass of approximately 36.96590 amu and a natural abundance of 24.23%.

Using the formula:

Atomic Mass = (34.96885 amu × 0.7577) + (36.96590 amu × 0.2423)

Atomic Mass = 26.4959 + 8.9560

Atomic Mass = 35.4519 amu

This calculated value closely matches the atomic mass of Chlorine found on the periodic table (typically rounded to 35.453 amu).

Use the calculator above to determine the atomic mass of any element by inputting the mass and relative abundance of its known isotopes. Remember that the sum of all isotope abundances should ideally be 100%.