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 observations from his α-particle scattering experiments as follows: (a) Most α particles not being deflected through the gold foil indicated that atoms are mostly empty space with a small, dense, positively charged nucleus at the center. (b) A few α particles being deflected at large angles suggested a strong repulsive force between the positively charged α particles and the atomic nucleus. If beryllium foil were used instead of gold, we would expect fewer α particles to be deflected at large angles due to its smaller nucleus, a larger spread of scattering angles, and possibly a need for adjusting the thickness of the foil.

Step-by-step solution

Observation (a) - Most α particles were not deflected

In Rutherford's scattering experiments, the fact that most α particles were not deflected as they passed through the gold foil led him to conclude that the atoms in the gold foil were mostly empty space. Since these positively charged α particles passed through without significant deviation, Rutherford concluded that the positively charged mass (protons) in an atom must be concentrated in a very small area at the center of the atom, called the nucleus. The electrons would then orbit around this small core of positive charge, occupying a majority of the atom's volume and leaving it largely empty.

Observation (b) - A few α particles were deflected at large angles

The observation that a few α particles were deflected at very large angles indicated that there was a very strong repulsive force between the positively charged α particles and some part of the atom. This led Rutherford to conclude that the positive charge (and also most mass) in the atom was concentrated in a small, dense nucleus. When an α particle came close to this nucleus, the repulsive force between the two positively charged entities caused the deflection at large angles.

Observation (c) - Differences with beryllium foil

If beryllium foil were used instead of gold foil in the α-particle scattering experiment, we would expect some differences in the results: 1. The number of α particles that would be deflected at large angles would likely decrease. This is because beryllium has a lower atomic number (4) compared to gold (79) and thus has fewer protons and a less massive nucleus. As a result, the repulsive force experienced by the α particles as they approach the beryllium nuclei would be lower, making it less likely for the α particles to be deflected at large angles. 2. The overall scattering pattern might have a larger spread. Since beryllium atoms are lighter than gold atoms, the α particles would have a greater chance of transferring more of their kinetic energy to the beryllium nuclei during a collision. This could result in a larger spread of scattering angles for the α particles. 3. The thickness of the foil required for the experiment might need to be adjusted, as the lower atomic weight of beryllium could affect the stopping power of the foil, potentially allowing more α particles to pass through without significant deflection.

Key concepts

Rutherford's Experiment

Rutherford's experiment is famously known for his groundbreaking work to explore the atomic nature using alpha-particle scattering. It occurred in the early 20th century when Ernest Rutherford aimed to test the existing model of the atom, which was based on the "plum pudding" model proposed by J.J. Thomson.
This previous model suggested that atoms consisted of electrons distributed within a "soup" of positive charge, comparable to raisins in a pudding.
Rutherford's experiment involved directing a beam of positively charged alpha particles at a thin sheet of gold foil. The results were surprising and led to new revelations about atomic structure. The vast majority of alpha particles passed straight through the foil with minimal deflection, indicating that atoms are mostly empty space.
Some particles, however, deflected at steep angles. This scattered the initial belief and led to the conclusion of a dense core in atomic structure. The experimental setup consisted of

• A source of alpha particles.
• A thin gold foil target.
• A detection screen to observe the scattering of these alpha particles.

Rutherford's findings revolutionized the understanding of the atomic world and firmly moved away from previous theories.

Atomic Structure Theory

Atomic structure theory helps us understand how atoms are composed and how they function. Before Rutherford's experiment, the "plum pudding" model of the atom was accepted, which posited that an atom was a large blob of positive charge within which electrons resided. However, Rutherford's findings turned the tables.
Upon observing that most alpha particles passed through without significant deflection, it was concluded that the atom is not solid, but instead consists mostly of empty space. The deflection of a small portion of alpha particles at large angles suggested a dense, positively charged center, which was later termed the nucleus.
Hence, the Rutherford model proposed that:

• Atoms have a small, dense, and positively charged nucleus.
• Electrons orbit this nucleus, similar to how planets orbit the sun.
• Most of the volume of an atom is empty space with electrons scattered throughout.

This sparked further research leading to the development of the more comprehensive quantum mechanical models of the atom we have today.

Nuclear Model of the Atom

Rutherford's experiment laid the foundation for the nuclear model of the atom. This model revolutionized our understanding of atomic structure by suggesting that atoms contain a small, dense, positively charged nucleus where most of the atom's mass and positive charge is concentrated.
This model explained a key aspect of the large angle deflections observed in alpha particle scattering experiments. The alpha particles, which are also positively charged, experienced a strong repulsive force when they passed close to this nucleus. This was due to the like-charge repulsion, causing them to be deflected at large angles.
The nuclear model suggested several key features:

• The nucleus contains both protons and (later discovered) neutrons.
• Electrons orbit the nucleus in defined paths.
• Atoms are mostly empty space, with a very small, but massive nucleus at the core.

This model was a pivotal step leading to the modern understanding of the atom. It paved the way for discoveries such as the existence of neutrons by James Chadwick and the development of quantum mechanics to better explain electron arrangements around the nucleus.