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Nuclei is short, modern and generous in JEE Main. Binding energy from a mass defect, nuclear size and the energy released in fission and fusion make up nearly every question. None of it needs deep thinking, only the right constant and a little care with the exponentials. Ten questions below. Give them ten honest minutes.
What this chapter carries in JEE Main
- Usually 1 to 2 questions every year, which is 4 to 8 marks.
- Binding energy from a mass defect is the regular one.
- Nuclear size, nuclear density, fission and fusion fill the rest.
What the syllabus says
In the syllabus (Unit 18, Atoms and Nuclei): Composition and size of the nucleus, atomic masses, the mass–energy relation, mass defect, binding energy per nucleon and how it varies with mass number, nuclear fission and fusion.
Taken out in 2024: isotopes, isobars and isotones; radioactivity — alpha, beta and gamma rays and their properties; the radioactive decay law, and with it half-life, mean life and activity.
Taken from the NTA syllabus for JEE Main 2027. See the full syllabus, unit by unit.
Formulas you must know by heart
| Nuclear radius | R = R0A1/3, R0 = 1.2 fm |
| Mass–energy conversion | 1 u = 931.5 MeV |
| Binding energy | BE = Δm × 931.5 MeV |
| Energy per fission of U-235 | about 200 MeV |
| Nuclear force | short range, very strong, charge independent |
| Q value of a reaction | Q = (mass of reactants − mass of products) × 931.5 MeV |
| Peak of the binding energy curve | about 8.8 MeV per nucleon, near A = 56 |
| Nuclear density | about 2.3 × 10¹⁷ kg/m³, the same for every nucleus |
Keep two numbers ready: 931.5 MeV for one atomic mass unit, and about 8.8 MeV per nucleon at the peak of the binding energy curve. Most questions in this chapter are one line of arithmetic once those two are in place.
Ten questions. Give yourself ten minutes.
Write your answers down before you scroll. A question you looked up is a question you have not answered.
Q1. A nucleus has a mass defect of 0.1 u. Its binding energy is about
- (a) 9.3 MeV
- (b) 93.15 MeV
- (c) 931.5 MeV
- (d) 0.93 MeV
Q2. The ratio of the radii of two nuclei of mass numbers 27 and 8 is
- (a) 3 : 2
- (b) 27 : 8
- (c) 9 : 4
- (d) 2 : 3
Q3. The binding energy per nucleon is highest for nuclei of mass number near
- (a) 4
- (b) 56
- (c) 120
- (d) 235
Q4. In a nuclear reaction, the quantity that is NOT conserved is
- (a) charge
- (b) mass number
- (c) rest mass
- (d) momentum
Q5. Nuclear density
- (a) rises with mass number
- (b) falls with mass number
- (c) is nearly the same for every nucleus
- (d) is proportional to the atomic number
Q6. The energy released in a single fission of uranium-235 is about
- (a) 2 MeV
- (b) 20 MeV
- (c) 200 MeV
- (d) 2000 MeV
Q7. Energy is released in both fission and fusion because in each case
- (a) the total number of nucleons falls
- (b) the products have a higher binding energy per nucleon than the reactants
- (c) charge is not conserved
- (d) the nuclear force becomes long ranged
Q8. The mass of a nucleus is always less than the total mass of its nucleons. This difference
- (a) is a measurement error
- (b) appears as the binding energy of the nucleus
- (c) is the mass of the electrons
- (d) is the kinetic energy of the nucleus
Q9. The energy of the sun is produced mainly by
- (a) the fission of heavy nuclei
- (b) the fusion of light nuclei
- (c) chemical burning
- (d) gravitational contraction
Q10. The force between two nucleons inside a nucleus is
- (a) dependent on their charge
- (b) short ranged and the same for any pair of nucleons
- (c) long ranged like gravity
- (d) weaker than the gravitational force
Answer key, with a hint for each
| Q1 | (b) | 0.1 × 931.5 MeV. |
| Q2 | (a) | R ∝ A1/3, so (27/8)1/3 = 3/2. |
| Q3 | (b) | The curve peaks near iron, A ≈ 56, at about 8.8 MeV per nucleon. Everything lighter can gain by joining, everything heavier by splitting. |
| Q4 | (c) | Some rest mass turns into energy. That missing mass is exactly where the energy comes from. |
| Q5 | (c) | R ∝ A^(1/3), so volume goes as A. Mass also goes as A, so the ratio stays fixed at about 2.3 × 10¹⁷ kg/m³. |
| Q6 | (c) | About 200 MeV, which is why a tiny mass of fuel yields so much energy. |
| Q7 | (b) | Both move towards the peak of the binding energy per nucleon curve — heavy nuclei by splitting, light nuclei by joining. |
| Q8 | (b) | Mass defect × 931.5 gives the binding energy in MeV. Nothing is lost — the mass has become energy. |
| Q9 | (b) | Four hydrogen nuclei build one helium nucleus, and the lost mass appears as energy. |
| Q10 | (b) | It acts only over a few femtometres, and a proton–proton pair feels it exactly as a proton–neutron pair does. |
Now mark yourself honestly
JEE Main marks the way it marks. Use the same rule here:
- +4 for a right answer
- −1 for a wrong one
- 0 for a blank
So ten questions here are out of 40. In the real paper, 25 Physics questions are out of 100.
If you scored 32 or more, the basics of this chapter are secure. Move to harder questions, not more of these.
If you scored below 24, do not feel bad about it. You have just found out something useful before the exam did. Go back to the formula table above, learn it properly, and sit these ten again tomorrow.
And if you guessed a few and they landed, count those as wrong. A guess that works once will not work in January.
The full chapter, on a clock
Ten questions tell you a little. Twenty-five tell you the truth.
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