E = m c² (Einstein, 1905). Mass and energy are interconvertible. 1 u = 931.5 MeV/c².
-- NCERT Class 12 Physics, Ch. 13, p. 310Mass Energy Relation
8 MCQs1 revision card9-step worked example
Source: NCERT Atoms and NucleiPYQ coverage: NEET 2020, 2026Official key: NTA-verifiedLast updated: 23 Sep 2026
Mass Energy Relation, explained for NEET
The recurring wrong answer on a mass–energy question is arithmetic, not conceptual. The past-paper record for this topic documents one distractor family: the student multiplies the mass by c instead of c². The result still looks impressively large, so it does not trigger the "that can't be right" reflex — and it is wrong by a factor of 3.00 × 10⁸.
The statement itself is short. NCERT Class 12 Physics, Chapter 13 (Nuclei), page 309 gives Einstein's relation as E = mc²: mass is a form of energy. Two consequences follow, and NEET tests both.
First, a body of mass m at rest already possesses energy mc² — its rest energy — with no motion, no field, no reaction required.
Second, conservation of mass and conservation of energy are no longer two separate laws. They merge into a single law of conservation of mass–energy. When a system gives up energy E to its surroundings, its rest mass falls by exactly E/c². That happens when a candle burns as surely as when a nucleus splits; only in the nuclear case is the mass change large enough to measure. (The atomic-mass-unit form of this, 1 u ≡ 931.5 MeV/c², is handled in the Atomic masses lesson — use it whenever the mass is given in u.)
Numerically, c² = 9.00 × 10¹⁶ m² s⁻² when c = 3.00 × 10⁸ m s⁻¹. That factor is the whole reason a microgram matters.
For NEET, this topic supplies roughly two questions every five papers — a light load, but an easy mark. The documented pattern is single-step and takes about 30 seconds, with medium negative-marking risk, which is another way of saying the errors are careless ones.
Watch out for three things: squaring c; the direction of the change (energy released means mass lost); and unit pairing — kilograms go with joules, atomic mass units go with MeV. Never mix the two halves of that pairing inside one substitution.
Can you answer these Mass Energy Relation MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
Einstein's mass–energy relation requires that the classical laws of conservation of mass and conservation of energy be replaced by the statement that
Show answer and why every option is right or wrong
Answer: C. C is correct. NCERT Class 12 Physics, Chapter 13 (Nuclei), page 309 states that since mass is a form of energy, the two classical conservation laws are generalised into one law of conservation of mass–energy.
Why A is wrong: A is wrong because it keeps mass conservation as an independent exact law, which is precisely what E = mc² overturns; energy conservation is not restricted to mechanical processes either.
Why B is wrong: B is wrong because mass is not discarded — it enters the conserved quantity as its energy equivalent mc². The relation unifies the two laws rather than deleting one.
Why D is wrong: D is wrong because it splits the single law into two domain-specific laws. The same unified law governs chemical and nuclear processes alike; only the size of the mass change differs.
MCQ 2Easy RecallPractice
For a body of mass m that is at rest, the quantity mc² is called
Show answer and why every option is right or wrong
Answer: A. A is correct. The mass–energy relation on page 309 of NCERT Class 12 Physics, Chapter 13 assigns every mass an equivalent energy mc², present whether or not the body moves; for a body at rest this is its entire energy.
Why B is wrong: B is wrong because kinetic energy is zero for a body at rest, while mc² is not. Rest energy is exactly the part of the energy that survives when all motion is removed.
Why C is wrong: C is wrong because no body with mass can be accelerated to the speed of light, so this work is not a finite defined quantity; mc² is the energy content of the mass itself, not a work done on it.
Why D is wrong: D is wrong because there is no threshold to cross. Any energy added to a system raises its mass immediately by that energy divided by c².
MCQ 3Easy RecallPractice
The relation E = mc² applies to
Show answer and why every option is right or wrong
Answer: D. D is correct. NCERT Class 12 Physics, Chapter 13, page 309 presents mass–energy equivalence as a general relation between mass and energy, not a rule confined to one class of reaction; the mass change in non-nuclear processes is simply too small to measure.
Why A is wrong: A is wrong because it mistakes where the effect is measurable for where it is valid. A burning candle also loses rest mass, by an amount far below any balance's resolution.
Why B is wrong: B is wrong because it confuses rest energy with relativistic kinetic effects. A stationary body has rest energy mc²; no high speed is required for the relation to hold.
Why C is wrong: C is wrong because annihilation is only the extreme case, in which the entire rest mass appears as photon energy. The relation is not restricted to it.
MCQ 4Direct ApplicationPractice
A mass of 1.00 × 10⁻³ kg is completely converted into energy. Taking c = 3.00 × 10⁸ m s⁻¹, the energy released is
Show answer and why every option is right or wrong
Answer: B. B is correct. E = mc² = (1.00 × 10⁻³)(9.00 × 10¹⁶) = 9.00 × 10¹³ J, using the relation stated on page 309 of NCERT Class 12 Physics, Chapter 13.
Why A is wrong: A is wrong because it evaluates mc rather than mc² — the documented distractor for this pattern. It is short of the correct value by a factor of 3.00 × 10⁸.
Why C is wrong: C is wrong because it is c² alone; the mass factor of 1.00 × 10⁻³ has been dropped from the product.
Why D is wrong: D is wrong because it divides by c² instead of multiplying. That operation answers the reverse question — the mass equivalent of a given energy.
MCQ 5Direct ApplicationPractice
An electron and a positron, both essentially at rest, annihilate and produce photons. Taking the rest energy of an electron as 0.511 MeV and that of a positron as equal to it, the total energy carried away by the photons is
Show answer and why every option is right or wrong
Answer: C. C is correct. Both particles are at rest, so the entire available energy is the sum of the two rest energies: 2 × 0.511 = 1.02 MeV, by the mass–energy relation of NCERT Class 12 Physics, Chapter 13, page 309.
Why A is wrong: A is wrong because it counts one particle only. The positron carries rest energy equal to the electron's, and both masses vanish in the annihilation.
Why B is wrong: B is wrong because it halves one rest energy instead of doubling it — the per-photon share only if a single 0.511 MeV were split between two photons, which is not what is asked.
Why D is wrong: D is wrong because 931.5 MeV is the energy equivalent of one atomic mass unit, a quantity roughly 1800 times an electron mass; it has no role in this calculation.
MCQ 6Direct ApplicationPractice
A process releases 4.50 × 10¹³ J of energy to its surroundings. Taking c = 3.00 × 10⁸ m s⁻¹, the rest mass of the system
Show answer and why every option is right or wrong
Answer: D. D is correct. Energy leaving the system lowers its rest mass by Δm = E/c² = (4.50 × 10¹³)/(9.00 × 10¹⁶) = 5.00 × 10⁻⁴ kg, which is the conservation of mass–energy described on page 309 of NCERT Class 12 Physics, Chapter 13.
Why A is wrong: A has the right magnitude but the wrong direction: a system that gives up energy loses rest mass, it does not gain it.
Why B is wrong: B is wrong because it divides by c rather than c², the same missing-square error that the past-paper record flags for this topic.
Why C is wrong: C is wrong because it multiplies the energy by c² instead of dividing. Multiplying is the mass-to-energy direction; this question runs the other way.
MCQ 7CalculationPractice
The Sun radiates energy at a steady rate of 3.90 × 10²⁶ W. Taking c = 3.00 × 10⁸ m s⁻¹, the rate at which its rest mass decreases is closest to
Show answer and why every option is right or wrong
Answer: A. A is correct. In one second the Sun radiates 3.90 × 10²⁶ J; by E = mc² that energy corresponds to Δm = (3.90 × 10²⁶)/(9.00 × 10¹⁶) = 4.33 × 10⁹ kg, so the mass falls at 4.33 × 10⁹ kg s⁻¹ (NCERT Class 12 Physics, Chapter 13, page 309).
Why B is wrong: B is wrong because it divides by c instead of c². Dropping the square is the error this topic's past-paper record singles out.
Why C is wrong: C is wrong because it multiplies the radiated energy by c² rather than dividing; that converts in the wrong direction and returns a mass larger than the Sun itself.
Why D is wrong: D is wrong because the exponent has been inverted. Dividing 3.90 × 10²⁶ by 9.00 × 10¹⁶ raises the power of ten to +9, not −9.
MCQ 8Concept TrapPractice
A metal block absorbs 4.20 × 10³ J of heat and its temperature rises. Taking c = 3.00 × 10⁸ m s⁻¹, the correct statement about its rest mass is that it
Show answer and why every option is right or wrong
Answer: B. B is correct. Energy added to a system raises its rest mass by E/c² = (4.20 × 10³)/(9.00 × 10¹⁶) ≈ 4.67 × 10⁻¹⁴ kg. The unified mass–energy law of NCERT Class 12 Physics, Chapter 13, page 309 applies to thermal energy exactly as it does to nuclear energy; only the scale differs.
Why A is wrong: A is wrong because rest mass tracks total energy content, not particle count. Adding energy without adding particles still raises the mass.
Why C is wrong: C is wrong because it has the sign backwards. Mass falls when energy leaves a system; here energy has entered it.
Why D is wrong: D is wrong because it makes the mass change conditional on a later event. The mass rises at the moment the energy is absorbed, whatever happens afterwards.
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Mass Energy Relation: quick recall before you leave
How do you solve a Mass Energy Relation question? A worked example
- 1
Given.
Rest-mass difference between reactants and products, Δm = 1.50 × 10⁻⁶ kg (products lighter).
Speed of light, c = 3.00 × 10⁸ m s⁻¹.
Conversion 1 kWh = 3.6 × 10⁶ J (exact, by definition). - 2
Required.
The energy released, in joules and in kilowatt-hours.
- 3
Concept.
The products are lighter than the reactants. That missing rest mass has not disappeared — by conservation of mass–energy it has left the system as energy. The magnitude of the released energy is fixed by the mass–energy relation of NCERT Class 12 Physics, Chapter 13, page 309.
- 4
Formula.
E = (Δm)c²
- 5
Substitution.
E = (1.50 × 10⁻⁶ kg)(3.00 × 10⁸ m s⁻¹)²
- 6
Calculation.
c² = (3.00 × 10⁸)² = 9.00 × 10¹⁶ m² s⁻²
E = (1.50 × 10⁻⁶)(9.00 × 10¹⁶) = 1.35 × 10¹¹ J
In kilowatt-hours: (1.35 × 10¹¹)/(3.6 × 10⁶) = 3.75 × 10⁴ kWh.
Note on constants: the factor 3.6 × 10⁶ J per kWh is exact by definition (1000 W × 3600 s, both exact counts), so it places no limit on significant figures. Only Δm and c are measured values, each to three significant figures, so the answers are quoted to three. - 7
Final answer.
E = 1.35 × 10¹¹ J ≈ 3.75 × 10⁴ kWh.
- 8
Common trap.
Multiplying by c once instead of c² gives 4.50 × 10² J — the documented distractor for this pattern, low by a factor of 3.00 × 10⁸. Two habits kill it: write c² = 9.00 × 10¹⁶ on the page as a separate line before substituting, and sanity-check that a microgram-scale mass yields an energy of order 10¹¹ J, not a few hundred. The second trap is unit pairing: Δm in kilograms must go with an answer in joules. If the mass had been given in u, the route is 931.5 MeV per u instead.
- 9
Similar NEET-style question.
A body at rest has rest energy 1.50 × 10⁻¹⁰ J. Taking c = 3.00 × 10⁸ m s⁻¹, its mass is closest to
(a) 5.00 × 10⁻¹⁹ kg (b) 1.67 × 10⁻²⁷ kg (c) 1.35 × 10⁷ kg (d) 4.50 × 10⁻² kg
Answer: (b). m = E/c² = (1.50 × 10⁻¹⁰)/(9.00 × 10¹⁶) = 1.67 × 10⁻²⁷ kg — roughly a proton mass. Option (a) divides by c only.
What to remember before solving Mass Energy Relation questions
Which Mass Energy Relation formulas do you need for NEET?
1 formula — click to collapse
Mass-energy equivalence
Einstein's mass-energy relation. 1 atomic mass unit = 931.5 MeV in energy units.
| Symbol | Quantity | SI Unit |
|---|---|---|
| E | energy | J or MeV |
| m | mass | kg or u |
| c | speed of light | m/s |
Valid when
- Conversion of mass to energy (or vice versa)
More in Atoms and Nuclei: 3 exam traps and mistakes · 5 formulas · 4 question patterns from its other lessons.
Mass Energy Relation questions from past NEET papers
2 questions from NEET 2020, 2026. Answers verified against NTA official keys. — click to collapse
NEET 2026
13726
23730
33736
43740
NTA Answer: Option 1(final)
NEET 2020
The energy equivalent of 0.5 g of a substance is :
10.5 × 10¹³ J
24.5 × 10¹⁶ J
34.5 × 10¹³ J
41.5 × 10¹³ J
NTA Answer: Option 3(final)
How does NEET ask about Mass Energy Relation?
1 recurring pattern from past papers — click to collapse
E = mc². Convert mass to energy or vice versa. 1 u → 931.5 MeV.
Direct ApplicationEasy
Common distractors
forgets c squared
Treats E = mc not mc²
Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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