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
| Symbol | Meaning | SI unit |
|---|---|---|
| E | energy released | J |
| m | mass defect | kg |
| c | speed of light | m s⁻¹ |
Rearrangements
m = E / c²c = √(E / m)
Worked example
Common trap
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)