Question

How did Rutherford interpret the following observations made during his \(\alpha\)-particle scattering experiments? (a) Most \(\alpha\) particles were not appreciably deflected as they passed through the gold foil. (b) A few \(\alpha\) particles were deflected at very large angles. (c) What differences would you expect if beryllium foil were used instead of gold foil in the \(\alpha\)-particle scattering experiment?

Short answer

Rutherford interpreted the observation that most α-particles were not appreciably deflected as evidence for the existence of a large amount of empty space inside atoms. The observation that a few α-particles were deflected at very large angles indicated the existence of a small, dense, positively charged nucleus at the center of the atom. If beryllium foil were used instead of gold foil, we would expect the likelihood of large deflection angles to be lower due to fewer protons and less densely packed nucleus in beryllium, and the percentage of α-particles passing through with minimal deflections might be higher due to the smaller nucleus and larger empty space in beryllium atoms.

Step-by-step solution

Rutherford's Interpretation for Observation (a)

In Rutherford's experiment, it was observed that most of the α-particles were not appreciably deflected, and passed straight through the gold foil with very minimal deflection angles. Rutherford interpreted this observation as evidence for the existence of a large amount of empty space inside the atom, because if atoms had been uniformly dense, more particles would have been deflected significantly.

Rutherford's Interpretation for Observation (b)

In Rutherford's experiment, it was observed that a few of the α-particles were deflected at very large angles, even bouncing straight back. Rutherford interpreted this observation as evidence for the existence of a small, extremely dense, positively charged nucleus at the center of the atom. The positively charged α-particles would be repelled by the positively charged nucleus, causing them to be deflected at large angles when they came close to the nucleus.

Expected differences with beryllium foil

If beryllium foil were used in place of gold foil in the α-particle scattering experiment, we would expect some differences due to the different atomic structure of beryllium compared to gold. Beryllium has a lower atomic number (4) than gold (79), which means its nucleus has fewer protons and is therefore less densely packed than gold's nucleus. This could lead to the following differences: 1. The likelihood of identifying a large deflection angle for the α-particles could be lower, as the fewer protons and less densely packed nucleus of beryllium may repel the α-particles with a lower force due to its weaker electrostatic force. 2. The percentage of α-particles that pass through the beryllium foil with minimal deflections might be higher compared to the gold foil experiment, due to the smaller size of the nucleus and the larger empty space in beryllium atoms.

Key concepts

atomic structure

The atomic structure is the arrangement of particles within an atom. Atoms are composed of three primary subatomic particles: protons, neutrons, and electrons. Protons and neutrons form the atom's nucleus, while electrons orbit at various energy levels around the nucleus.
One key feature of atomic structure is that most of the atom's mass is concentrated in the nucleus because protons and neutrons are much heavier than electrons. Electrons are light and occupy most of the atom's volume, which means there's a lot of empty space within an atom.
Rutherford's experiment was crucial in going beyond the then-popular plum pudding model, which suggested atoms had much more evenly spread mass and charge. Instead, his findings illuminated the true structure with a dense central nucleus.

nucleus

The nucleus is the dense, positively charged center of an atom. It contains two types of subatomic particles: protons, which are positively charged, and neutrons, which have no charge. The strong nuclear force binds these particles together, making the nucleus highly dense.
Rutherford's scattering experiment significantly altered our understanding of the nucleus. The experiment showed that the nucleus occupies only a small region in the atom but holds most of its mass. This insight helped to correct earlier misconceptions and led to the nuclear model of the atom, laying the groundwork for modern atomic theory.
Since the nucleus contains protons, the total charge of the nucleus is positive, which plays a vital role in the interaction with other particles, such as alpha particles in scattering experiments.

alpha particles

Alpha particles are positively charged particles consisting of two protons and two neutrons, identical to the nucleus of a helium atom. In Rutherford's experiment, alpha particles were used to probe the internal structure of the atom.
The choice of alpha particles was due to their relatively large mass and positive charge, which makes them effective at testing the forces within the atom. As they pass through material, they interact with other charged particles, particularly protons in the atomic nucleus.
These particles travel in straight lines unless acted upon by a force, thus making large deflections rare but revealing when they occur, providing a powerful means to infer the distributions of mass and charge in atoms.

deflection angles

In the context of scattering experiments, deflection angles refer to the angle at which particles veer off their original paths when they encounter other particles. During Rutherford's experiment, most alpha particles passed through the foil with little to no deflection, while a small fraction deflected at large angles.
The angles of deflection provide insights into the internal structure of the atom. Small deflections suggest minimal interference, implying that particles find little concentrated charge or mass.
However, large deflections indicate encounters with dense, concentrated charges within the atom's nucleus. This clear distinction in deflection angles was critical for Rutherford's conclusion of a concentrated nuclear region within the atom.

electrostatic force

The electrostatic force is the force of attraction or repulsion between charged particles. In the context of Rutherford's experiment, this force was significant. Since both the alpha particles and the atomic nuclei carry positive charges, they repel each other due to the electrostatic force.
When an alpha particle comes close to an atomic nucleus, the repelling electrostatic force can cause it to deviate from its path. The strength of the deflection depends on the proximity of the alpha particle to the nucleus and the total charge of the nucleus.
This force is described by Coulomb's Law, which states that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Understanding this force was crucial for interpreting the scattering patterns in Rutherford's experiment.