Final answer:
In Bohr's model, only transitions between whole-number energy levels are allowed. Thus, transitions c) n = 1 to n = 2 and d) n = 2 to n = 1 are permitted, while a) and b) with fractional levels are not.
Step-by-step explanation:
In the context of Bohr's model of the atom, the only allowed energy transitions are those where the electron moves from one whole-number energy level (orbit) to another, such as from n = 1 to n = 2, or from n = 2 to n = 1. These levels are quantized, meaning they are discrete and not fractional. Therefore, transitions a) n = 2 to n = 2.5 and b) n = 1 to n = 1.5 are not allowed because they involve fractional energy levels, which are not permissible in Bohr's model.
Transitions c) from n = 1 to n = 2 and d) from n = 2 to n = 1 are allowed because they involve movement between whole-number orbits. When an electron moves to a lower energy level, such as from n = 2 to n = 1, energy is released in the form of a photon. The energy of this photon can be calculated using the Bohr formula for the energy difference between the two levels.