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How to Calculate Atomic Mass of an Atom
Understanding how to calculate atomic mass is a fundamental skill in chemistry. While we often see a single number on the periodic table, that number represents a weighted average of all the naturally occurring isotopes of that element.
What is Atomic Mass?
Atomic mass (often called atomic weight) is the mass of a single atom, usually expressed in atomic mass units (amu). One amu is defined as 1/12th the mass of a carbon-12 atom.
There are two primary ways to look at atomic mass:
- Mass Number: The sum of protons and neutrons in a specific nucleus. This is always a whole number (e.g., Carbon-12 has 6 protons and 6 neutrons).
- Average Atomic Mass: The weighted average mass of all isotopes of an element. This is the decimal number you see on the periodic table (e.g., Carbon's is 12.011).
The Atomic Mass Formula
To calculate the average atomic mass, you multiply the mass of each isotope by its fractional abundance and then sum the results.
Average Atomic Mass = (Mass₁ × Abundance₁) + (Mass₂ × Abundance₂) + … + (Massₙ × Abundanceₙ)
Note: Abundance must be used as a decimal (e.g., 75% = 0.75).
Step-by-Step Calculation Example
Let's calculate the average atomic mass of Chlorine using its two main isotopes:
| Isotope |
Mass (amu) |
Natural Abundance |
| Chlorine-35 |
34.969 amu |
75.77% (0.7577) |
| Chlorine-37 |
36.966 amu |
24.23% (0.2423) |
The Calculation:
- Convert percentages to decimals: 75.77% → 0.7577 and 24.23% → 0.2423.
- Multiply Mass 1 by Abundance 1: 34.969 × 0.7577 = 26.496 amu
- Multiply Mass 2 by Abundance 2: 36.966 × 0.2423 = 8.957 amu
- Add the products: 26.496 + 8.957 = 35.453 amu
Why Isn't Atomic Mass a Whole Number?
Atomic mass is rarely a whole number because it factors in multiple isotopes with varying masses and their relative frequency in nature. Even for a single isotope, the mass is not exactly a whole number because of the "mass defect"—the energy that holds the nucleus together results in a slight loss of mass according to Einstein's E=mc².
Tips for Accurate Calculation
- Check your units: Ensure all masses are in atomic mass units (amu).
- Abundance Check: Ensure your total abundance adds up to 100% (or 1.00 in decimal form).
- Significant Figures: Chemistry problems often require you to round your final answer to the correct number of significant figures based on the input data.
function calculateAtomicMass() {
// Get values from inputs
var m1 = parseFloat(document.getElementById('mass1').value);
var a1 = parseFloat(document.getElementById('abundance1').value);
var m2 = parseFloat(document.getElementById('mass2').value);
var a2 = parseFloat(document.getElementById('abundance2').value);
var resultBox = document.getElementById('result-box');
var resultText = document.getElementById('result-text');
var warning = document.getElementById('abundance-warning');
// Validation
if (isNaN(m1) || isNaN(a1) || isNaN(m2) || isNaN(a2)) {
alert('Please enter valid numbers for all fields.');
return;
}
// Calculation Logic
// Atomic Mass = (Mass1 * Abundance1/100) + (Mass2 * Abundance2/100)
var weighted1 = m1 * (a1 / 100);
var weighted2 = m2 * (a2 / 100);
var totalMass = weighted1 + weighted2;
// Check if abundance totals 100%
var totalAbundance = a1 + a2;
if (Math.abs(totalAbundance – 100) > 0.1) {
warning.style.display = 'block';
warning.innerHTML = 'Warning: Total abundance is ' + totalAbundance.toFixed(2) + '%. It should usually equal 100%.';
} else {
warning.style.display = 'none';
}
// Display Results
resultText.innerHTML = totalMass.toFixed(5) + ' amu';
resultBox.style.display = 'block';
}