Evans SPH 4U1

Physics Grade 12

Unit 9: Quantum Theory

Note 7: Rutherford's Model of the Atom

Reference: Chapter 12.3

Early Greeks (400B.C.) thought matter was composed of atoms.  At the beginning of the 20th century a scientist J.J. Thomson proposed that the inside of an atom was made up of a positively charged sphere with negative electrons embedded in it ('raisins in a bun model'). However, it was really Ernest Rutherford who made the first true experiments and discoveries of what the internal structure of an atom might be.

Rutherford Experiment:

He performed experiments in which alpha particles (from radioactive polonium) were fired through a very thin gold foil (10^-7m or about 400 gold atoms thick). The structure of the atom was found be observing the directions in which the alpha particles were scattered as they passed through the gold foil.

He found the following:

1. Most of the alpha particles passed straight through the gold foil un-deflected.

2. The alpha particles lost energy in passing through the gold foil.

3. Only about 1 out of every 10 000 alpha particles was deflected by more than 10 degrees.

4. In extremely rare cases, an alpha particle was deflected by more than 90 degrees.

5. The foil acquired a positive charge after a long exposure to the beam of alpha particles.

From these observations he concluded:

1. Most of the atom's volume is empty space (since most of the particles were un-deflected).

2. Since occasional large deflections were seen, the alpha particles must have been acted upon by strong forces. Therefore, somewhere in the atom there is a large massive core containing most of the mass of the atom - the nucleus.

3. Most of the atom's volume is empty space but within this space are negatively charged electrons moving in orbits around the nucleus.

Trajectory of the Alpha Particles:

Rutherford tried to analyze the deflected particles and their trajectories.

He knew that alpha particles were positive and his model said that the atom's positive charge was concentrated in the nucleus.  He therefore reasoned that the force causing the scattering was a Coulomb force of repulsion between the alpha particle and the nucleus.

Recall:

The path is a hyperbola with the nucleus at one of the foci..

Charge on the Nucleus:

A nucleus of different mass would not effect the trajectory of the alpha particle, however,  it would affect the size of the Coulomb force and therefore the scattering angle.

A nucleus with a larger charge (larger atomic number) would cause a larger force to be exerted on the alpha particle, causing greater deflection.

The number of alpha particles scattered at a given angle is proportional to the square of the charge.

Size of the Nucleus (or distance of closest approach):

Rutherford reasoned that an alpha particle with 0 aiming error (i.e. one directed right at the tiny nucleus) would slow down to a momentary stop before retracing its steps.

It had been established that the force of repulsion between the alpha particle and the gold nucleus was a coulomb force (force inversely proportional to r squared).  This enabled Rutherford to express the electric potential energy in measurable terms.  He also knew the initial Ek of the alpha particle.  At the point of closest approach – when the alpha particle came to a momentary stop – all of its initial Ek was converted to potential energy.  From this Rutherford was able to determine the distance of closest approach.

DEMO: Pretend a student is a gold nucleus (79 positive charges).  Teacher pretend she is an alpha particle. When the alpha particle is released she has lots of kinetic energy.  As she approaches the student she slows down and says that she is losing kinetic energy and gaining potential energy.