The correct option is Option B: spectrum of an atom or ion containing one electron only.

The Bohr Model, proposed by Niels Bohr in 1913, attempts to explain the atomic structure and the quantization of energy levels. The model was specifically developed to describe the hydrogen atom, the simplest atom consisting of only one electron. However, the principles of the Bohr Model can be generalized to any atom or ion that contains only one electron moving around a nucleus. This includes not only the hydrogen atom (which has one proton and one electron) but also singly ionized helium (He+), doubly ionized lithium (Li2+), and so on, where each of these ions has only one electron. The reason the Bohr Model works for these systems is that the system's physics is dominated by the interaction between the single electron and the nucleus, which can be described using the same quantization rules Bohr proposed.

The Bohr Model cannot accurately describe:

Option A: The spectrum of hydrogen atom only - This option is partially true but incomplete. The Bohr Model does explain the hydrogen spectrum, but it is not limited to only hydrogen.

Option C: The spectrum of the hydrogen molecule - The Bohr Model does not apply to molecules, including the hydrogen molecule (H2), because molecules involve more complex interactions between multiple electrons and nuclei that the model does not account for.

Option D: The solar spectrum - The solar spectrum is generated by the light emitted from the Sun, which includes a wide variety of atoms and molecules in different states. The Bohr Model cannot explain the solar spectrum because it is only applicable to atoms or ions with a single electron.

In conclusion, the Bohr Model is applicable and can explain the spectra of atoms or ions that contain only a single electron (Option B), because its foundational assumptions are based on the quantized orbits of an electron around a nucleus in such systems.