By J.R. Kambak, updated August 30, 2022

Atomic mass units (amu) provide a convenient way to express the mass of subatomic particles. To convert amu into the SI energy unit joule (J), we rely on Einstein’s mass‑energy equivalence: E = m c². This short guide walks you through the conversion step by step, including a real‑world example with lithium‑7.

Step‑by‑Step Conversion of 1 amu to Joules

1. Recognize the mass defect

The mass of a nucleus is always less than the sum of its constituent protons and neutrons. Accurate mass measurements are essential; rounding early can eliminate the tiny mass defect.

2. Convert amu to kilograms

Use the precise conversion: 1 amu = 1.66053886 × 10⁻²⁷ kg.

3. Apply Einstein’s equation

Insert the mass defect (here 1 amu) and the speed of light (c = 2.99792458 × 10⁸ m s⁻¹) into E = m c²:

E = 1.66053886 × 10⁻²⁷ kg × (2.99792458 × 10⁸ m s⁻¹)²

4. Compute the energy

Carrying out the calculation yields E = 1.492393 × 10⁻¹⁰ kg m² s⁻².

5. Convert to joules

Since 1 kg m² s⁻² equals 1 J, the final result is:

1 amu = 1.492393 × 10⁻¹⁰ J

Example: Binding Energy of Lithium‑7

1. Determine the mass defect

• Nuclear mass of ⁷Li = 7.014353 amu • Total mass of its nucleons: (3 × 1.007276) + (4 × 1.008665) = 7.056488 amu • Mass defect = 7.056488 – 7.014353 = 0.042135 amu

2. Convert to kilograms

0.042135 amu × 1.66053886 × 10⁻²⁷ kg = 6.99693 × 10⁻²⁸ kg

3. Calculate the energy

E = 6.99693 × 10⁻²⁸ kg × (2.99792458 × 10⁸ m s⁻¹)² = 6.28842 × 10⁻¹² J

Thus, the binding energy of lithium‑7 is approximately 6.29 × 10⁻¹² J.

These calculations illustrate how the mass defect translates directly into binding energy, underscoring the profound link between mass and energy described by relativity.