Rutherford Experiment
Rutherford Experiment
The Rutherford Experiment, also known as the Rutherford Gold Foil Experiment, was a groundbreaking experiment conducted by Ernest Rutherford in 1909 that led to the discovery of the atomic nucleus. This experiment was pivotal in the development of the nuclear model of the atom.
The Experiment
Rutherford, along with his assistants Hans Geiger and Ernest Marsden, directed a beam of alpha particles (helium nuclei) at a thin sheet of gold foil. They observed the scattering of the alpha particles after they hit the foil using a fluorescent screen. The screen would glow when struck by an alpha particle, allowing the team to detect the particles' paths.
Observations
Most alpha particles passed straight through the foil with little to no deflection. However, a small number of particles were deflected at large angles, and a very few even bounced back towards the source.
Interpretation
Rutherford concluded that the atom must consist of a small, dense nucleus containing most of the atom's mass, surrounded by a cloud of electrons. This nucleus was responsible for the large-angle deflections of the alpha particles.
Rutherford's Nuclear Model
Based on his observations, Rutherford proposed a model of the atom with the following features:
- A central nucleus that is positively charged and contains most of the atom's mass.
- Electrons orbiting the nucleus at relatively large distances.
- The size of the nucleus is very small compared to the overall size of the atom.
Differences from Previous Models
The table below outlines the differences between Rutherford's model and the plum pudding model proposed by J.J. Thomson:
| Feature | Rutherford's Model | Plum Pudding Model |
|---|---|---|
| Structure | Nucleus with electrons orbiting around it | Uniform positive sphere with electrons embedded |
| Mass Distribution | Concentrated in the nucleus | Spread throughout the atom |
| Size of Positive Charge | Very small (nucleus) | Large (entire atom) |
| Electron Arrangement | Orbiting the nucleus | Randomly distributed |
Formulas and Calculations
Rutherford's experiment did not directly involve complex formulas, but the scattering of alpha particles can be described by the Rutherford scattering formula:
[ \frac{d\sigma}{d\Omega} = \left(\frac{1}{4\pi\epsilon_0}\right)^2 \frac{Z_1^2 Z_2^2 e^4}{(4E)^2} \frac{1}{\sin^4(\theta/2)} ]
where:
- (\frac{d\sigma}{d\Omega}) is the differential cross-section for scattering.
- (\epsilon_0) is the vacuum permittivity.
- (Z_1) and (Z_2) are the atomic numbers of the alpha particle and the gold nucleus, respectively.
- (e) is the elementary charge.
- (E) is the kinetic energy of the alpha particles.
- (\theta) is the scattering angle.
Examples
Example 1: Scattering Angle
If an alpha particle with a kinetic energy of 5 MeV is deflected by a gold nucleus at an angle of 60 degrees, what is the differential cross-section for this scattering?
Given:
- (Z_1 = 2) (for helium)
- (Z_2 = 79) (for gold)
- (E = 5 \times 10^6 \times 1.602 \times 10^{-19}) J (conversion from eV to J)
- (\theta = 60^\circ)
Using the Rutherford scattering formula, we can calculate the differential cross-section.
Example 2: Probability of Scattering
Using the Rutherford scattering formula, one can calculate the probability of an alpha particle being deflected by a certain angle when passing near a gold nucleus. This probability is related to the differential cross-section.
Conclusion
The Rutherford Experiment was a significant milestone in the field of atomic physics. It disproved the plum pudding model and led to the acceptance of the nuclear model of the atom. This experiment also paved the way for further research into the structure of the atom, ultimately leading to the development of quantum mechanics.