JEE Main Physics Atoms & Nuclei 2027: Bohr Model, Hydrogen Spectrum & Binding Energy

From a scattered alpha particle to the energy of the Sun: Atoms & Nuclei covers an entire journey in one chapter. JEE Main questions are largely formula-driven, so this is a chapter where preparation converts directly into marks.

Energy levels are negative because the electron is bound. Zero energy means free.

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Chapter at a Glance

Priority reflects past-paper trends, not an official NTA weightage.

What the NTA Syllabus Covers

• Alpha-particle scattering experiment, Rutherford's model, Bohr model, energy levels, hydrogen spectrum
• Composition and size of the nucleus, atomic masses, mass-energy relation, mass defect
• Binding energy per nucleon and its variation with mass number, nuclear fission and fusion

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Master These Topics

1. Rutherford's Nuclear Atom

Alpha particles fired at gold foil mostly passed straight through, but a few bounced back sharply. Conclusion: an atom has a tiny, dense, positively charged nucleus containing almost all the mass, with electrons outside. The distance of closest approach for an alpha particle of kinetic energy K is r₀ = 2kZe² / K.

2. Bohr Model of Hydrogen-like Atoms

For an atom with atomic number Z and orbit number n:

• Radius: r_n = 0.529 n² / Z angstrom
• Energy: E_n = −13.6 Z² / n² eV
• Speed: v_n = 2.19 × 10⁶ Z / n m/s
• Angular momentum: mvr = nh/2π

Worked example (Balmer H-alpha line): For the transition n = 3 to n = 2 in hydrogen, ΔE = 13.6 (1/4 − 1/9) = 13.6 × 5/36 ≈ 1.89 eV. Wavelength = 1240 / 1.89 ≈ 656 nm, a red visible line.

Spectral series in hydrogen:

The general formula is 1/λ = RZ² (1/n₁² − 1/n₂²) with R = 1.097 × 10⁷ m⁻¹.

Trap: Energy of a bound electron is negative. A larger n means a less negative (higher) energy, so the electron moves out and the atom absorbs energy.

3. The Nucleus: Size, Mass Defect and Binding Energy

Nuclear radius follows R = R₀A^(1/3) with R₀ ≈ 1.2 fm, which implies nuclear density is roughly the same for all nuclei.

The mass of a nucleus is less than the sum of its nucleons. This mass defect Δm converts to binding energy through E = Δm c², where 1 u = 931.5 MeV/c².

Worked example: For the deuteron, Δm ≈ 0.0024 u, so the binding energy is 0.0024 × 931.5 ≈ 2.2 MeV, or about 1.1 MeV per nucleon.

4. Binding Energy Curve, Fission and Fusion

Binding energy per nucleon rises steeply for light nuclei, peaks at about 8.7 to 8.8 MeV near mass number 56 (the iron region), then falls slowly for heavy nuclei.

• Fission: a heavy nucleus splits into medium-mass nuclei with higher binding energy per nucleon, releasing energy.
• Fusion: light nuclei combine into a heavier one, again moving up the curve, releasing energy.

The unit description in the NTA syllabus does not name radioactive decay explicitly, so treat half-life questions as a lower-priority bonus rather than a core focus.

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Common Traps to Avoid

• Forgetting the Z² factor when using the Bohr energy formula for He⁺ or Li²⁺.
• Confusing the series (Lyman, Balmer, Paschen) with their spectral regions.
• Using atomic masses instead of the correct combination when computing mass defect.
• Treating binding energy per nucleon and total binding energy as the same thing.

60-Second Revision Sheet

• E_n = −13.6 Z²/n² eV, r_n = 0.529 n²/Z Å
• Lyman UV (n=1), Balmer visible (n=2), Paschen IR (n=3)
• R = R₀A^(1/3), R₀ = 1.2 fm; 1 u = 931.5 MeV
• Peak of binding energy curve near iron (A around 56)

Your Study Plan

1. Day 1: Rutherford scattering and Bohr formulas.
2. Day 2: hydrogen spectrum problems, including hydrogen-like ions.
3. Day 3: mass defect, binding energy and Q-value of reactions.
4. Day 4: fission, fusion and a timed mixed set.

Practice Atoms & Nuclei Questions Free → (opens in a new tab)

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Continue Your Physics Journey

• Previous chapter: Dual Nature of Matter & Radiation
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• All 20 JEE Main Physics chapters
• Complete JEE Main Syllabus 2027 guide

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