Rutherford's Experiment - Size of the Nucleus

Understanding the fundamental structure of matter is essential to Physics. Figuring out the size of the nucleus which is the crux of this article would not be possible without the Rutherford gold foil experiment. The Rutherford model of the atom was the first correct interpretation of the atom and it laid the groundwork for Bohr to build his interpretation on.

Rutherford Gold Foil Experiment

Before Rutherford’s experiment, the best model of the atom that was known to us was the Thomson or “plum pudding” model. In this model, the atom was believed to consist of a positive material “pudding” with negative “plums” distributed throughout. Later, Rutherford’s alpha-particle scattering experiment changed the way we think of the atomic structure. Rutherford directed beams of alpha particles at thin gold foil to test this model and noted how the alpha particles scattered from the foil.

In the experiment, Rutherford showed us that the atom was mainly an empty space with the nucleus at the centre and electrons revolving around it. When alpha particles were fired towards the gold foil, Rutherford noticed that 1 in 20000 particles underwent a change in direction of motion of more than 90 degrees. The rest 19999 particles deviated from their trajectory by a very small margin. This led to a conclusion that the atom consisted of an empty space with most of the mass concentrated at the centre in tiny volumes. This volume at the centre was named as ‘the nucleus’; Latin for ‘little nut’.

Through this experiment, Rutherford made 3 observations as follows:

• Highly charged alpha particles went straight through the foil undeflected. This would have been the expected result for all of the particles if the plum pudding model was correct.
• Some alpha particles were deflected back through large angles.
• A very small number of alpha particles were deflected backwards! To this Rutherford remarked, “It was as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back at you!”

To explain these observations, a new model of the atom was needed. In the new model, the positive material was considered to be concentrated in a small but massive region called the nucleus. Electrons were considered to be revolving around the nucleus preventing one atom from trespassing on its neighbour’s space to complete this model.

Size of the Nucleus

It was possible to obtain the size of the nucleus through Rutherford’s experiment. We can calculate the size of the nucleus, by obtaining the point of closest approach of an alpha particle. By shooting alpha particles of kinetic energy 5.5 MeV, the point of closest approach was estimated to be about 4×10-14m. Since the repulsive force acting here is Coulomb repulsion, there is no contact. This means that the size of the nucleus is smaller than 4×10-14m.

The sizes of the nuclei of various elements have been accurately measured after conducting many more iterations of the experiment. Having done this, a formula to measure the size of the nucleus was determined.

$R$ =$R_0 A^{\frac{1}{3}}$

Where R0 = 1.2×10-15m.

From the formula, we can conclude that the volume of the nucleus which is proportional to R3 is proportional to A (mass number). Another thing to be noticed in the equation is that there is no mention of density in the equation. This is due to the fact that the density of the nuclei does not vary with elements.  The density of the nucleus is approximately 2.3×1017 kg.m-3.

• What did RutherFord’s gold foil experiment teach us about the atomic structure?

Rutherford’s gold foil experiment showed us that the atom is mostly empty space with a comparatively tiny, massive, positively charged nucleus in the centre.

• What caused the alpha particles to deflect in Rutherford’s gold-foil experiment?

Rutherford thought that the particles would fly straight through the foil. However, he found that the path of the particle would be shifted or deflected when passing through the foil. This is due to the fact that like charges repel each other.

• How did Rutherford’s experiment affect our world?

Rutherford’s experiment provided us with a better, more practical understanding of matter. The experiment provided conclusive evidence against previous conceptions of matter and provided a new model consistent with the facts.

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