Final answer:
Considering all intermediate states, a hydrogen atom in the n = 6 state can emit 10 different photon energies as it transitions to the ground state. The calculation is based on the number of different paths the electron can take to reach the ground state.
Step-by-step explanation:
The question asks how many different photon energies can be emitted by a hydrogen atom transitioning from the n = 6 state to the ground state, where n is the principal quantum number. Given the quantum mechanical nature of the atom, the number of possible transitions is determined by the number of available energy levels between the initial and final states.
For a hydrogen atom in the n = 6 level, it can transition to the n levels of 5, 4, 3, 2, and 1 (ground state). The transitions are:
- n=6 to n=5
- n=6 to n=4
- n=6 to n=3
- n=6 to n=2
- n=6 to n=1
Each transition emits a photon of a specific energy, equating to 5 different photon energies. However, to count all possible paths, the atom can transition through intermediate states. For example, the atom can go from n=6 to n=5 and then from n=5 to n=1, which creates additional paths. Therefore, we have to consider all these intermediate transitions to determine all possible paths.