Which one of the following conclusions could not be derived from Rutherford's α-particle scattering experiment?
Electrons move in a circular path of fixed energy called orbits
Understanding Rutherford's α-Particle Scattering Experiment
Rutherford's α-particle scattering experiment, also known as the Geiger-Marsden experiment, was a landmark experiment that provided crucial insights into the structure of the atom. In this experiment, a beam of positively charged alpha (α) particles was directed at a thin gold foil. The way these particles scattered after hitting the foil was observed and analyzed.
Observations from the α-Particle Scattering Experiment
The main observations from the experiment were:
- Most of the α-particles passed straight through the gold foil without any deflection.
- Some α-particles were deflected by small angles.
- A very small fraction of α-particles (~1 in 20,000) were deflected by large angles, and a few even bounced back (deflected by nearly 180 degrees).
Conclusions Drawn from Rutherford's Experiment
Based on these observations, Rutherford proposed his nuclear model of the atom. Let's analyze what conclusions were derived:
- Most of the space in the atom is empty: Since most α-particles passed straight through, it implied that the particles did not encounter any obstacle. This observation led to the conclusion that the majority of the volume within an atom is empty space. This conclusion was directly supported by the experimental data.
- Nearby all the mass of the atom resides in the nucleus: The large-angle deflection and backscattering of a few α-particles indicated that they encountered a very dense and massive object within the atom. This object must also be positively charged to repel the positively charged α-particles. Rutherford concluded that nearly all the mass and all the positive charge of an atom are concentrated in a very small region at the center, which he called the nucleus.
- The nucleus is very small compared to the atom: The fact that only a very small fraction of α-particles were significantly deflected or bounced back showed that the dense, positively charged region (the nucleus) is extremely small compared to the overall size of the atom. Calculations based on the scattering data allowed Rutherford to estimate the size of the nucleus to be about \(10^{-15}\) m, while the atomic radius is about \(10^{-10}\) m.
The ratio of the atomic radius to the nuclear radius is approximately:
$$ \text{Ratio} = \frac{\text{Atomic Radius}}{\text{Nuclear Radius}} \approx \frac{10^{-10} \text{ m}}{10^{-15} \text{ m}} = 10^5 $$Thus, the radius of the atom is about \(10^5\) times the radius of the nucleus. This conclusion was derived from the experiment.
Analyzing the Options
Let's evaluate each given option based on whether it could be derived from Rutherford's α-particle scattering experiment:
-
Most of the space in the atom is empty
This conclusion is directly supported by the large number of α-particles that passed through the foil undeflected. So, this could be derived.
-
The radius of the atom is about 10 5times the radius of the nucleus
This relative size estimation of the nucleus versus the atom was a quantitative conclusion derived from the scattering data analysis. So, this could be derived.
-
Electrons move in a circular path of fixed energy called orbits
Rutherford's model proposed electrons orbiting the nucleus, similar to planets around the sun. However, his model did not include the concept of fixed energy levels or specified orbits with definite energies. This idea of fixed energy orbits was introduced later by Niels Bohr in his model to explain the stability of the atom and atomic spectra. Therefore, this conclusion could not be derived from Rutherford's scattering experiment.
-
Nearby all the mass of the atom resides in the nucleus
The large deflections and backscattering indicated a dense, massive nucleus at the center, where most of the mass is concentrated. So, this could be derived.
Conclusion Not Derived from Rutherford's Experiment
Based on the analysis, the conclusion that "Electrons move in a circular path of fixed energy called orbits" is associated with the Bohr model of the atom, not Rutherford's model derived from the α-particle scattering experiment. Rutherford's model had a stability problem because, according to classical physics, orbiting electrons (which are accelerating) should continuously lose energy by radiation and spiral into the nucleus.
Therefore, the conclusion that could not be derived from Rutherford's α-particle scattering experiment is that electrons move in circular paths of fixed energy called orbits.
| Observation | Conclusion Derived |
|---|---|
| Most \(\alpha\)-particles undeflected | Most space in atom is empty. |
| Few \(\alpha\)-particles deflected by small angles | There is a positively charged center (nucleus). |
| Very few \(\alpha\)-particles deflected by large angles or bounced back | Positive charge and mass concentrated in a tiny, dense nucleus. |
| - | Atomic radius \(\approx 10^5 \times\) Nuclear radius. |
Revision Table: Atomic Models
| Model | Key Features | Contribution | Limitations (Relevant here) |
|---|---|---|---|
| Thomson's Plum Pudding Model | Positive charge spread uniformly, electrons embedded. | First model to incorporate electrons. | Could not explain \(\alpha\)-scattering results (large deflections). |
| Rutherford's Nuclear Model | Dense positive nucleus at center, electrons orbit it, mostly empty space. | Discovery of the nucleus, empty space concept, size estimation. | Could not explain atomic stability or discrete atomic spectra. Did not propose fixed energy orbits. |
| Bohr's Model | Electrons orbit nucleus in specific stable orbits (energy levels) without radiating energy. | Explained atomic stability and hydrogen spectrum using quantization of energy. | Applicable mainly to hydrogen and hydrogen-like ions, could not explain spectra of multi-electron atoms or fine structure. |
Additional Information on Rutherford Scattering
Rutherford's scattering formula mathematically describes the number of alpha particles scattered at different angles. This formula depends on the charge of the alpha particle, the charge of the nucleus (atomic number of the target material), the kinetic energy of the alpha particle, and the scattering angle. The agreement between the experimental data and this formula provided strong support for the nuclear model and allowed for the determination of the nuclear charge (and hence atomic number) of the target element.
The concept of "fixed energy called orbits" belongs specifically to the Bohr model, which refined Rutherford's model by incorporating quantum ideas to address its shortcomings, particularly the stability of the atom and the origin of atomic spectra.
Important Questions from Alpha-particle Scattering
A proton and an an alpha particle are accelerated through different potential differences such that their final kinetic energies are identical. If the mass of an alpha particle ($m_\alpha$) is approximately four times the mass of a proton ($m_p$), what is the ratio of the de Broglie wavelength of the proton to that of the alpha particle ($\lambda_p : \lambda_\alpha$)?
Which phenomenon deals with the scattering of light by molecules of a medium when they are excited to vibrational energy levels?
