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Rutherford's Nuclear Model of Atom & Alpha-Particle Scattering Notes

Rutherford's Nuclear Model of Atom & Alpha-Particle Scattering

Detailed explanation of the alpha-particle scattering experiment conducted by Geiger and Marsden under Rutherford's guidance, leading to the nuclear model of the atom. Covers experimental observations, estimation of nuclear size via distance of closest approach, impact parameter, and model limitations.

Class 12 Science
JEE
NEET
Physics
English · 7 topics
Checked against the video on 23 Oct 2026

Made by AI from the YouTube video Class 12 Chapter 12 ii Atoms 01: Alpha Particle Scattering & Rutherford Model Of Atom JEE/NEET (opens YouTube in a new tab) by Physics Wallah - Alakh Pandey, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Rutherford's Nuclear Model of Atom & Alpha-Particle Scattering

English7 topics · 5 MCQs · 10 flashcardsWatch the video (opens YouTube in a new tab)

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In short

Detailed explanation of the alpha-particle scattering experiment conducted by Geiger and Marsden under Rutherford's guidance, leading to the nuclear model of the atom. Covers experimental observations, estimation of nuclear size via distance of closest approach, impact parameter, and model limitations.

Introduction and Historical Background

Ernest Rutherford performed initial experiments on alpha particles in 1906, before directing his students to conduct a detailed study.
Must knowIn 1911, Hans Geiger and Ernst Marsden performed the definitive alpha-particle scattering experiment on the suggestion of Ernest Rutherford.
Ernest Rutherford was historically a student of J. J. Thomson, who discovered the electron.

Experimental Setup of Alpha-Particle Scattering

A radioactive source such as bismuth (Bi) kept inside a lead cavity emits alpha particles.
The energy of naturally emitted alpha particles from the source ranges from about 5 MeV to 7.7 MeV.
Lead bricks are used to absorb stray radiation and collimate alpha particles into a fine, thin beam.
The collimated beam strikes a thin gold foil having a thickness of about 10⁻⁶ m to 10⁻⁸ m, representing approximately a single layer of gold atoms.
Gold is chosen specifically for the target foil because of its exceptional malleability, allowing extremely thin sheets.
Must knowScattered alpha particles hit a circular zinc sulfide (ZnS) screen, producing tiny flashes of light (scintillations) detected using a movable microscope.

Observations of the Scattering Experiment

Must knowAbout 99.86% of the alpha particles pass straight through the gold foil undeviated (deflection angle theta approximately 0 degrees).
Only about 0.14% of the alpha particles deviate by more than 1 degree.
Approximately 1 in 8,000 alpha particles deflects by more than 90 degrees.
Must knowOnly about 1 in 10⁶ (one in a million) alpha particles suffers a deflection of nearly 180 degrees and retraces its path.
An alpha particle is a doubly ionized helium ion (He²+), consisting of 2 protons and 2 neutrons, with a charge of +2e and mass of 4 u.
Rutherford formulated an empirical relationship for the number of particles scattered: N(theta) is proportional to 1 / sin⁴(theta / 2).

Rutherford's Nuclear Model of Atom

Most of the space inside an atom is empty because over 99% of alpha particles pass through without deviation.
Positive charge inside the atom is not spread throughout (disproving J. J. Thomson's plum pudding model), but concentrated in an extremely tiny region called the nucleus.
Must knowThe size of an atom is of the order of 10⁻¹⁰ m, while the size of a nucleus is estimated around 10⁻¹⁵ m (making the atom ~10⁵ times larger).
The positive charge of a nucleus is +Ze, differing across metals and depending on atomic number Z.
Must knowElectrons revolve around the nucleus in circular orbits where the necessary centripetal force is provided by the electrostatic force of attraction (Fe = Fc).

Distance of Closest Approach

At the distance of closest approach (r0), the entire initial kinetic energy of the head-on alpha particle converts into electrostatic potential energy.
Must knowThe formula for distance of closest approach is: r0 = (2 × Z × e²) / (4 × pi × epsilon_0 × K.E).
For gold (Z = 79) and natural maximum kinetic energy (7.7 MeV), r0 calculates to approximately 30 fm (3 × 10⁻¹⁴ m).
The actual radius of a gold nucleus must be less than this distance of closest approach, and is experimentally found to be around 6 fm.

Impact Parameter

Must knowImpact parameter (b) is the perpendicular distance of the initial velocity vector of the alpha particle from the center of the nucleus.
When the impact parameter is very small (b -> 0), the alpha particle experiences a direct head-on collision and scatters backwards (theta -> 180 degrees or pi).
When the impact parameter is large (b >> r0), the electrostatic repulsion is weak and the particle passes virtually undeflected (theta -> 0 degrees).
Impact parameter is given by: b = (k × Z × e² / K.E) × sqrt((1 + cos(theta)) / (1 - cos(theta))), where b is typically expressed in fermi.

Drawbacks of Rutherford's Model

Must knowRutherford's model cannot explain the stability of the atom according to classical electromagnetic theory (Maxwell's theory).
A revolving electron undergoes continuous centripetal acceleration and must continuously emit energy as radiation.
Losing energy would cause the electron to spiral inward and crash into the nucleus in approximately 10⁻⁸ seconds.
Must knowThe model cannot explain the discrete (line) spectrum of atoms, because arbitrary orbital radii would imply a continuous emission spectrum.

Key terms

Alpha Particle: A doubly ionized helium atom (He²+) composed of two protons and two neutrons, with charge +2e and mass 4 u.
Distance of Closest Approach (r0): The minimum distance between an incoming head-on alpha particle and the nucleus at which its kinetic energy becomes zero.
Impact Parameter (b): The perpendicular distance between the initial velocity vector of an alpha particle and the center of the target nucleus.
Centripetal Acceleration: Acceleration directed towards the centre of a circular path, possessed by revolving electrons in Rutherford's model.

Formulas

N(theta) = (K × Z²) / sin⁴(theta / 2): Calculates number of alpha particles scattered at scattering angle theta
r0 = (1 / (4 × pi × epsilon_0)) × (2 × Z × e² / K.E): Distance of closest approach for a head-on alpha collision
Fe = Fc => (1 / (4 × pi × epsilon_0)) × (Z × e² / r²) = (m × v² / r): Equilibrium condition for electron revolving around nucleus
b = (k × Z × e² / K.E) × sqrt((1 + cos(theta)) / (1 - cos(theta))): Impact parameter related to scattering angle theta

Quick revision

Read these the night before the exam.

Geiger and Marsden carried out the alpha-particle scattering experiment in 1911 under Rutherford.
About 99.86% of alpha particles pass through the foil undeflected.
Approximately 1 in 10⁶ alpha particles suffers a deflection of around 180 degrees.
Target gold foil thickness in the experiment was around 10⁻⁶ m to 10⁻⁸ m.
The scintillation screen used in the scattering experiment is coated with zinc sulfide (ZnS).
Estimated size of a nucleus is ~10⁻¹⁵ m compared to atomic size of ~10⁻¹⁰ m.
If impact parameter b -> 0, scattering angle theta approaches 180 degrees.
Classical electromagnetic theory predicts an accelerated electron should collapse into the nucleus within 10⁻⁸ s.
The actual radius of a gold nucleus is about 6 fm.

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