Alpha-particle Scattering and Rutherford’s Nuclear Model of Atom

Geiger and Marsden performed the scattering experiment on a thin gold foil in 1909 under the direction of Rutherford. In this experiment, alpha particles from a radioactive source were allowed to strike a thin gold foil with a thickness of about 2.1 × 10⁻⁷ m.

A small detector, placed at specific angles relative to the beam, detected the scattered alpha particles. The scattered alpha-particles produced scintillations on a zinc sulphide screen, which were observed through a microscope.

The main parts of the arrangement were:

• A radioactive source of alpha-particles, placed inside a lead box.
• A lead block with a hole, which provided a narrow beam of alpha-particles.
• A thin gold foil.
• A zinc sulphide fluorescent screen to detect scattered alpha-particles.
• A microscope to observe the scintillations on the screen.

The following observations were made in the alpha-particle scattering experiment:

1. Most of the alpha particles passed through the gold foil undeflected.
2. Some alpha particles were scattered through small angles.
3. About 0.14% of the incident alpha particles were scattered by more than 1°.
4. About 1 in 8000 alpha particles are deflected by more than 90^∘.

From the scattering data, Rutherford concluded that the positive charge and most of the mass of the atom are concentrated in a very small region at the centre of the atom. This central core was called the nucleus.

According to Rutherford's nuclear model:

• The positive charge and most of the mass of the atom are concentrated in the nucleus at the centre.
• The nucleus is much smaller than the atom.
• The size of the nucleus is of the order of 10⁻¹⁵ m to 10⁻¹⁴ m.
• The size of the atom is of the order of 10⁻¹⁰ m.
• Most of the space in the atom is empty.
• Electrons revolve around the nucleus.

In order to explain the scattering of alpha-particles by the nucleus, Rutherford made the following assumptions:

• The scattering takes place due to the repulsive Coulomb force between the alpha particle and the positively charged nucleus.
• The nucleus is so much heavier than the alpha particle that it remains stationary during scattering.
• Since the gold foil is thin, an alpha particle suffers only a single scattering.
• The charge on the alpha particle is 2e.
• If the atomic number of the element is Z, then the charge on the nucleus is Ze.
• For gold, Z = 79.

If the distance between the alpha-particle and the nucleus is rr, then the electrostatic force between them is given by:

F = \[\frac {1}{4πε_0}\] ⋅ \[\frac{2e\cdot Ze}{r^2}\]

• Geiger and Marsden carried out the alpha-particle scattering experiment under Rutherford's direction.
• Most alpha particles passed undeflected through the gold foil.
• A very small fraction of alpha-particles were deflected through large angles.
• Positive charge and most of the mass are concentrated in the nucleus.
• The nucleus is extremely small compared with the atom.
• Most of the atom is empty space.
• Electrons revolve around the nucleus.