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Exam level3 past questions

Rutherford scattering and atomic nucleus

Study the principles of Rutherford scattering, distance of closest approach, Coulomb force, and how these experiments revealed the structure and size of the nucleus.

Why this shows up in the exam

NEET often includes questions on nuclear size, scattering, and the forces inside atoms.

How NEET tests this

ApplicationStatement analysisNumerical

Learn the idea

Rutherford scattering shows that α‑particles are deflected by the Coulomb repulsion of a tiny, massive nucleus; the key insight is that the distance of closest approach is found by equating the projectile’s kinetic energy to the Coulomb potential energy.

🧠 Memory hook: Coulomb’s law is gravity’s electric twin – it pulls or pushes with strength that drops as 1 over r squared, just like the Sun’s gravity on planets.

Get this one clearly and it pays off every single time it shows up in the paper. 🎯

Formulas & facts to keep ready

  • Coulomb force F = (1/4πϵ0)·Z₁Z₂e² / r²
  • Coulomb potential energy U = (1/4πϵ0)·Z₁Z₂e² / r
  • Distance of closest approach r₀ = (1/4πϵ0)·Z₁Z₂e² / (K.E. of projectile)
  • Nuclear radius ≈ 1.2 fm·A^(1/3)
  • Atomic radius ≈ 1 Å (10⁻¹⁰ m)
  • Volume of atom ≈10¹⁵ times volume of nucleus

How to approach it

  1. 1Read the statement: is it about force law, distance of closest approach or size?
  2. 2Write the relevant formula from the key ideas (Coulomb law or r₀ expression).
  3. 3Substitute the given charges, energy or mass values; solve algebraically.
  4. 4If the question asks for a ratio, use typical radii (10⁻¹⁰ m vs 10⁻¹⁵ m) and cube the ratio.

Worked example — watch it click

Assertion (A): The force of repulsion between atomic nucleus and α-particle varies with distance according to inverse square law. Reason (R): Rutherford did α-particles scattering experiment.

  • A)Both (A) and (R) are true, and (R) is the correct explanation of (A).
  • ✅Both (A) and (R) are true, but (R) is not the correct explanation of (A).
  • C)(A) is true, but (R) is false.
  • D)Both (A) and (R) are false.

The concept behind this problem

The worked example checks whether you recognise that A states a physical law (inverse‑square force) while R is merely a historical fact; they are both true but R does not explain A.

Step by step

  1. 1Coulomb force F = kq₁q₂/r² follows inverse square law (A true).
  2. 2Rutherford did perform α-scattering experiment (R true).
  3. 3However, R is a historical fact, not an explanation of why the force follows inverse square law.
  4. 4The explanation is Coulomb's law itself.

Watch out

Students often answer that Rutherford’s experiment *explains* the inverse‑square law, forgetting that the law comes from Coulomb’s theory itself.

Common slip-ups that cost marks

  • •Confusing the inverse‑square dependence of force with the inverse‑linear dependence of potential energy
  • •Treating Rutherford’s experiment as the *reason* for Coulomb’s law rather than a verification
  • •Mixing up atomic radius (≈10⁻¹⁰ m) with nuclear radius (≈10⁻¹⁵ m) when estimating size ratios

🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.

Practise it

These are real questions from past NEET papers that test this exact idea.

Question 1 of 3NEET 2023

Assertion (A): The force of repulsion between atomic nucleus and α-particle varies with distance according to inverse square law. Reason (R): Rutherford did α-particles scattering experiment.

Push further

More challenging

8 harder questions built from the past papers above — a step up in difficulty, with distractors designed so you can't get there by elimination. Written and checked by our reviewers, not from a real paper.

Question 1 of 8

An alpha particle (charge +2e) with kinetic energy 5.0 MeV is directed towards a gold nucleus (atomic number 79). Calculate the distance of closest approach, assuming the gold nucleus remains stationary.

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