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Mass–energy equivalence Formula, SPM Physics

Formula: E = mc². Not given in the exam, recall it.

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Mass–energy equivalence
E = mc²

Not given in the exam, recall it.

What it is for

Mass–energy equivalence is used in Nuclear Physics (SPM Physics Form 5). Keep the SI units in every line of working. Nuclear Physics

Symbols and SI units

SymbolMeaningSI unit
Eenergy releasedJ
mmass defectkg
cspeed of lightm s⁻¹

Rearrangements

  • m = E / c²
  • c = √(E / m)

Worked example

A mass defect m = 2.0 × 10⁻³ kg is converted to energy (c = 3.0 × 10⁸ m s⁻¹). E = mc² = 2.0 × 10⁻³ × (3.0 × 10⁸)² = 1.8 × 10¹⁴ J.

Common trap

Square c (c² = 9.0 × 10¹⁶). m is the mass defect in kilograms, convert from grams or atomic mass units first.

Understanding Mass–energy equivalence

Einstein's relation E = mc² states that a change in mass releases energy. Here E is the energy released in joules (J), m is the mass defect (the mass that disappears) in kilograms (kg), and c is the speed of light, 3.0 × 10⁸ m s⁻¹.

The quantities relate because mass and energy are two forms of the same thing; in a nuclear reaction the tiny loss of mass reappears as a very large amount of energy, since c² is enormous (9.0 × 10¹⁶ m² s⁻²).

To rearrange, isolate the unknown: m = E / c² finds the mass defect from a known energy, and c = √(E / m) recovers the speed of light. Because c is squared, always square it before multiplying or dividing.

A worked example, step by step

In a nuclear reaction a mass defect of m = 3.0 × 10⁻⁴ kg is converted into energy. Find the energy released (c = 3.0 × 10⁸ m s⁻¹).

Apply E = mc², squaring c first:

c² = (3.0 × 10⁸ m s⁻¹)² = 9.0 × 10¹⁶ m² s⁻².

E = mc² = 3.0 × 10⁻⁴ kg × 9.0 × 10¹⁶ m² s⁻² = 2.7 × 10¹³ J.

The mass lost is minute, yet the energy is 27 trillion joules, showing how much energy is locked in mass. The energy released is 2.7 × 10¹³ J.

Common mistakes and how this is tested

The most common mistake is forgetting to square c, which makes the answer 10⁸ times too small. Another is leaving the mass in grams or in atomic mass units instead of converting to kilograms first.

A third is mixing powers of ten wrongly when handling standard form; keep the digits and the exponents separate.

Under calculate, show c² explicitly and substitute with units to reach joules. Under define, state that mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus.

Under explain, you may be asked why nuclear reactions release far more energy per kilogram than chemical reactions, which E = mc² makes clear.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English), Sijil Pelajaran Malaysia: Format Pentaksiran mulai 2021, Fizik (4531) (Bahagian Pembangunan Kurikulum (BPK), KPM)

Written by the spmphysics.com.my editorial team.· Updated 5 Sept 2026

Frequently asked questions

Is this formula given in the exam?
No. SPM Physics papers provide no formula sheet, so this must be recalled.
What is a mass defect?
It is the small amount of mass that seems to disappear when nucleons bind into a nucleus, or when a nucleus splits or fuses. That lost mass is converted into energy through E = mc².
Why is the energy released so large?
Because c² is 9.0 × 10¹⁶ m² s⁻², an enormous number. Even a tiny mass defect of a fraction of a gram gives an energy of many trillions of joules.
What units must I use in E = mc²?
Use mass in kilograms and the speed of light in metres per second, and the energy comes out in joules. Convert grams or atomic mass units to kilograms before substituting.

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