Final answer:
Both the Bohr model and the Rutherford model have a nucleus with electrons orbiting, but they differ in electron motion treatment; Bohr introduced quantized orbits for electron stability, unlike Rutherford's model.
Step-by-step explanation:
The Bohr model and the Rutherford model of the atom share some similarities but also have important differences. They are similar in that both involve a relatively heavy nucleus with electrons moving around it. However, they differ in their treatment of electron motion and the stability of these motions.
Rutherford's model, similar to a solar system, could not explain the stability of atoms since classical mechanics would predict that electrons in motion around the nucleus would eventually spiral in and collapse the atom. On the other hand, the Bohr model introduced quantized orbits for the electrons which could only have specific, stable orbits. These quantized orbits meant that electrons would only emit or absorb energy when jumping between orbits, creating a model that could predict the discrete spectra observed in experiments.
The correct answer to the student's question, based on the information provided, is option c: Both models propose the existence of a nucleus; different in their views on electron stability. This is because while both models account for a nucleus with orbiting electrons, Bohr's model allows for electron stability through quantized orbits.