A single hydrogen atom is initially prepared in the sixth Bohr orbit. It eventually reaches the ground state and is allowed to pass through intermediate stationary states. Find the maximum possible number of photons emitted by this one atom before it reaches the ground state.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A single hydrogen atom is initially prepared in the sixth Bohr orbit. It eventually reaches the ground state and is allowed to pass through intermediate stationary states. Find the maximum possible number of photons emitted by this one atom before it reaches the ground state.

Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model

G1 Physics · Accepted Answer

For one atom, the maximum number of photons is obtained when the electron loses only one principal quantum number at each step. Starting from n = 6, it can successively visit the fifth, fourth, third, second and first levels. That requires five separate energy-lowering transitions. Therefore the maximum number of emitted photons from one atom is 6−1 = 5. Hence N = 5.