Examples of Rutherford's scattering experiment observations

📚 Quick Study Guide

• ⚛️ Rutherford's scattering experiment involved firing alpha particles at a thin gold foil.
• 🔭 The experiment aimed to probe the structure of the atom.
• ✨ Most alpha particles passed straight through the foil, suggesting that atoms are mostly empty space.
• 💥 A small fraction of alpha particles were deflected at large angles, indicating the presence of a small, dense, positively charged nucleus.
• 📐 The angular distribution of the scattered alpha particles can be predicted by Rutherford's scattering formula: $ \frac{dn}{d\Omega} = \left( \frac{q_1 q_2}{16 \pi \epsilon_0 K} \right)^2 \frac{1}{\sin^4(\theta/2)} $, where $dn/d\Omega$ is the differential cross-section, $q_1$ and $q_2$ are the charges of the alpha particle and the nucleus, $K$ is the kinetic energy of the alpha particle, $\theta$ is the scattering angle, and $\epsilon_0$ is the permittivity of free space.
• 💡Key Observation: The number of alpha particles scattered at a given angle decreases rapidly as the angle increases.
• 🔬These observations led to the development of the Rutherford model of the atom, with a small, dense, positively charged nucleus surrounded by orbiting electrons.

Practice Quiz

1. Which of the following particles was used in Rutherford's scattering experiment?
   1. Alpha particles
   2. Beta particles
   3. Gamma rays
   4. Neutrons
2. What was the primary observation that led Rutherford to propose the nuclear model of the atom?
   1. Most alpha particles passed straight through the gold foil.
   2. All alpha particles were deflected at small angles.
   3. Some alpha particles were deflected at very large angles.
   4. No alpha particles were able to penetrate the gold foil.
3. What does the observation that most alpha particles passed straight through the gold foil suggest?
   1. The atom is mostly solid.
   2. The atom is mostly empty space.
   3. The atom has a uniform density.
   4. The atom contains a large number of neutrons.
4. What property of the nucleus was Rutherford able to determine based on the scattering data?
   1. Its color
   2. Its mass
   3. Its charge
   4. Its temperature
5. Which of the following is a consequence of Rutherford's scattering experiment?
   1. The discovery of the electron
   2. The development of the plum pudding model
   3. The discovery of the neutron
   4. The development of the nuclear model of the atom
6. According to Rutherford's scattering formula, how does the scattering rate change with the scattering angle $\theta$?
   1. It increases with increasing $\theta$.
   2. It decreases with increasing $\theta$.
   3. It is independent of $\theta$.
   4. It increases with $\sin(\theta)$.
7. If the kinetic energy of the alpha particles is doubled, what happens to the scattering rate at a particular angle?
   1. It doubles.
   2. It halves.
   3. It quadruples.
   4. It is reduced to one-fourth.