Notes : Rutherford, Geiger and Marsden Experiment (Alpha Particle Scattering Experiment) - Class 12 Physics

The Rutherford, Geiger and Marsden Experiment, also known as the Alpha Particle Scattering Experiment or Gold Foil Experiment, was performed in 1911. This experiment led to the discovery of the atomic nucleus and the development of Rutherford's Nuclear Model of the Atom.

Introduction

Ernest Rutherford, along with Hans Geiger and Ernest Marsden, conducted experiments to study the scattering of alpha particles by thin gold foils. The results of these experiments completely changed the understanding of atomic structure.

What is an Alpha Particle?

• An alpha particle is the nucleus of a helium atom.
• Charge on alpha particle = +2e
• Mass of alpha particle ≈ 4 times the mass of a proton

Experimental Setup

• Radioactive Source: Bi-214 was used as the source of alpha particles.
• Lead Block with Collimator: It produced a narrow beam of alpha particles.
• Thin Gold Foil: A gold foil of thickness approximately 2.1 × 10^-7 m was used.
• ZnS Screen: A zinc sulphide coated screen detected alpha particles by producing scintillations (flashes of light).
• Movable Microscope: Used to count the scintillations at different scattering angles.
• Vacuum Chamber: The experiment was conducted in vacuum to avoid scattering by air molecules.

Working of the Experiment

1. A narrow beam of alpha particles was directed towards the thin gold foil.
2. After passing through the foil, alpha particles scattered in different directions.
3. The scattered particles struck the ZnS screen and produced flashes of light.
4. The microscope was rotated to measure the number of scattered particles at different angles.

Observations

1. Most alpha particles passed through the gold foil without any deflection.
2. Some alpha particles (about 0.14%) were deflected through small angles (less than 1°).
3. A very small fraction (about 1 in 8000) were deflected through large angles greater than 90°.
4. Some alpha particles were even reflected back (180° scattering).
5. The number of scattered particles decreases rapidly with an increase in scattering angle.

Rutherford Scattering Formula

The number of alpha particles scattered per unit area at an angle θ is given by:

N(θ) ∝ 1 / sin⁴(θ/2)

This means that the number of scattered particles decreases as the scattering angle increases.

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Conclusions of Rutherford's Experiment

1. Most of the Atom is Empty Space

Since most alpha particles passed through the foil undeflected, Rutherford concluded that most of the space inside an atom is empty.

2. Presence of a Small, Dense Nucleus

The large-angle deflections indicated the presence of a very small, dense and positively charged region at the centre of the atom called the nucleus.

3. Nucleus Contains Most of the Mass

Backward scattering of alpha particles suggested that almost the entire mass of the atom is concentrated in the nucleus.

4. Electrons Exist Outside the Nucleus

Electrons occupy the space around the nucleus and do not significantly affect the motion of alpha particles because of their small mass.

Rutherford's Nuclear Model of Atom

• The atom consists of a small positively charged nucleus at its centre.
• Almost the entire mass of the atom is concentrated in the nucleus.
• Electrons revolve around the nucleus in circular orbits.
• Electrostatic attraction provides the centripetal force required for orbital motion.

Size of Atom and Nucleus

Quantity	Approximate Size
Radius of Atom	10-10 m
Radius of Nucleus	10-15 m to 10-14 m

Thus, an atom is approximately 10,000 to 100,000 times larger than its nucleus.

Coulomb Force Between Alpha Particle and Nucleus

$$F = \frac{1}{4πε} . \frac{(2e)(Ze)}{r^{2}}$$

Where:

• F = Electrostatic force
• Z = Atomic number of the target nucleus
• e = Electronic charge
• r = Distance between alpha particle and nucleus

Limitations of Rutherford's Model

1. Stability Problem: According to classical theory, electrons revolving around the nucleus should continuously lose energy and collapse into the nucleus.
2. Atomic Spectra: Rutherford's model could not explain the discrete line spectra of atoms.

Frequently Asked Questions (FAQs)

Q1. What is Rutherford's Alpha Particle Scattering Experiment?

It is an experiment in which alpha particles were directed towards a thin gold foil to study the internal structure of atoms.

Q2. Why was gold foil used in Rutherford's experiment?

Gold is highly malleable and can be beaten into extremely thin sheets, allowing alpha particles to pass through individual atomic layers.

Q3. What are scintillations?

Scintillations are tiny flashes of light produced when alpha particles strike a zinc sulphide (ZnS) screen.

Q4. Why was the experiment performed in vacuum?

Vacuum prevented alpha particles from scattering due to air molecules, ensuring accurate observations.

Q5. What did Rutherford conclude from the experiment?

He concluded that the atom contains a small, dense, positively charged nucleus and that most of the atom is empty space.

Q6. What is the charge on an alpha particle?

An alpha particle carries a charge of +2e.

Q7. What is the significance of backward scattering?

Backward scattering indicated the presence of a massive and positively charged nucleus at the centre of the atom.

Q8. What are the limitations of Rutherford's atomic model?

The model failed to explain atomic stability and the line spectra of atoms.

Summary

Rutherford's alpha particle scattering experiment revolutionized atomic physics by proving that atoms possess a tiny, massive and positively charged nucleus surrounded by mostly empty space.