Bohr's model can be used for hydrogen-like ions—ions that have only one electron, such as He⁺ and Li²⁺. (a) Why is the Bohr model applicable to He⁺ ions but not to neutral He atoms?

Verified step by step guidance

1. Understand the Bohr model: The Bohr model is specifically designed for systems where a single electron orbits a nucleus. It simplifies the electron-nucleus interaction by considering only one electron moving in a fixed orbit around the nucleus.
2. Recognize the electron configuration of He⁺ and neutral He: Helium (He) in its neutral state has two electrons. When it loses one electron, becoming He⁺, it has only one electron remaining.
3. Consider electron-electron interaction: In neutral helium, the presence of two electrons means that electron-electron repulsion must be considered, which complicates the system beyond what the Bohr model can accurately handle.
4. Apply the Bohr model to He⁺: Since He⁺ has only one electron, the system is simplified to a single electron orbiting the nucleus, similar to the hydrogen atom. This fits the conditions under which the Bohr model provides a good approximation.
5. Conclude why Bohr model is not applicable to neutral He: The Bohr model does not account for interactions between multiple electrons, which is necessary for accurately describing the behavior of neutral helium with its two electrons.

Key Concepts

Bohr's Model of the Atom

Bohr's model describes the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits. It quantizes the angular momentum of electrons, allowing only certain stable orbits. This model is particularly effective for hydrogen-like ions, where a single electron is influenced by the nucleus's charge.

Hydrogen-like Ions

Hydrogen-like ions are ions that contain only one electron, similar to hydrogen. Examples include He⁺ and Li²⁺. The simplicity of having a single electron allows for the application of Bohr's model, as the electron's behavior can be accurately predicted by the model's equations, unlike in multi-electron systems.

Electron-Electron Interactions

In neutral helium (He), there are two electrons that repel each other due to their negative charges. This electron-electron interaction complicates the energy levels and orbital shapes, making the Bohr model inadequate. The model does not account for these interactions, which are significant in multi-electron atoms, leading to deviations from the predictions made for hydrogen-like ions.