Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom: Explanation

In the year 1911, along with his assistants H. Geiger and E. Marsden, Rutherford, performed the experiment of Alpha Particle scattering, which led to the invention of the ‘nuclear model of an atom’ – a vital step towards how we see the atom today. The scientists performed an experiment whose schematic image is shown in the figure given below. At a thin metal foil made of gold, they directed a beam of 5.5 MeV α-particles emitted from a radioactive source. The beam was permitted to fall on a thin gold foil of thickness 2.1 × 10-7 m. Then through a rotatable detector consisting of a zinc sulphide screen and a microscope, the scattered alpha-particles were observed. On striking the screen, the scattered alpha particles produced brief light flashes or scintillations. These flashes can be viewed through a microscope and the distribution of the number of scattered particles may be studied as a function of the angle of scattering.

Observation of the Alpha (α) scattering Experiment:

It was observed that Many of the α-particles passed through the foil which concludes that they do not suffer any kind of collisions. Approximately around 0.14% of the incidents α-particles scatter by more than 10 and about 1 in 8000 deflect by more than 900.

The conclusion from the Alpha (α) scattering Experiment-

On the basis of the α scattering experiment, Rutherford had concluded the following important points.

According to Rutherford-

• The Scattering of alpha particle is because of the columbic force between positive charge of α particle and positive charge of atom.
• Rutherford’s experiments suggested the size of the nucleus to be about 10 m to 10–14 m.
• The electrons are present at a distance of about 10,000 to 100,000 times the size of the nucleus itself.
• Atoms have a lot of empty space and the entire mass of the atom is confined to a very small central core which is also known as a nucleus.

Impact Parameter:

It’s the perpendicular distance of the velocity vector of α particles from the central line of the nucleus, when the particle is far away from the nucleus of the atom.

The angle of scattering:

It‘s the angle formed by α particles when it gets deviated from its original path around the nucleus.

The Alpha Particle Scattering Experiment

For the experiment, They took a thin foil of gold having a thickness of around 2.1×10-7 m and kept it in the middle of a rotatable detector formed of zinc sulfide and a microscope. Then, they ejected a beam of 5.5MeV alpha particles at the foil from a radioactive source. This led to bricks collimating these alpha particles as they passed through them.

By the brief flashes on the screen after hitting the foil, the scattering of these alpha particles could be studied. Rutherford and his partners expected to learn more about the structure of the atom from the results of this particular experiment.

Observations

Here are the observations of the experiment:

• without suffering any collisions most of the alpha particles passed through the foil
• Around 0.14% of the incident alpha particles scattered by more than 1o
• Around 1 in 8000 alpha particles deflected by more than 90o

The following observations gave rise to many arguments and conclusions which formed the structure of the nuclear model on an atom.

Conclusions and arguments

The results and outcome of this experiment were not in sync with the plum-pudding model of the atom as suggested by Thomson. Rutherford concluded that as alpha particles are positively charged, so in order for them to be deflected back, they needed a large repelling force. He further said that for this to happen, the positive charge of the atom needs to be concentrated in the centre, unlike scattered in the earlier accepted model.

Therefore, when the incident alpha particle comes very close to the positive mass in the centre of the atom, it will repel giving rise to deflection. On the other side, if it passes through at a fair distance from this mass, then there will be no deflection and it would simply pass through.

Rutherford then suggested the ‘nuclear model of an atom’ in which the entire positive charge and most of the mass of the atom is concentrated within the nucleus. The electrons move in orbits around the nucleus like the planets and the sun. Rutherford also concluded from his experiments that the size of the nucleus is somewhere between 10-15 and 10-14 m.

In relation to the Kinetic theory, the size of an atom is around 10-10 m or around 10,000 to 100,000 times the size of the nucleus proposed by Rutherford. Therefore, the distance of the electrons from the nucleus should be around 10,000 to 100,000 times the size of the nucleus.

This eventually suggests that most of the atom is empty space and further explains why most alpha particles passed right through the foil. And also, these particles are deflected or scattered through a large angle on coming close to the nucleus. Also, the trajectory of these incident alpha particles is not affected by the electrons having negligible mass.

Alpha Particle Trajectory

The trajectory traced by an alpha particle is dependent upon the impact parameter of the collision. The impact parameter is basically the perpendicular distance of each alpha particle from the centre of the nucleus. The scattering of these particles depends solely on the impact parameter as in a beam, all the alpha particles have the same kinetic energy.

Therefore, the particles closer to the nucleus or the particles with a small impact parameter, experience a large angle of scattering. On the other side, those with a large impact parameter suffer no deflection or scattering at all. Finally, a head-on collision with the nucleus rebounds back or those particles having zero impact parameter.

Talking about the experiment, Rutherford and his team had noticed that a really very small fraction of the incident alpha particles were rebounding back. Hence, only a small number of particles were colliding head-on with the nucleus. This, eventually, made them believe that the mass of the atom is concentrated in a very small volume.

Electron Orbits

In short, Rutherford’s nuclear model of the atom describes it as:

• An electrically neutral sphere with
  • A positively charged small nucleus at the Centre.
  • Which, in their dynamically stable orbits is Surrounded by revolving electrons

The centripetal force that keeps the electrons in their orbits is a result of:

• The electrostatic force of attraction between-
  • The positively charged nucleus and
  • The negatively charged revolving electrons.