A large collection of hydrogen atoms is initially in the ground state. Each atom absorbs a photon of energy 12.09 eV, which excites it to the third Bohr orbit. The atoms are then allowed to de-excite through all possible paths. Find the maximum number of distinct emission lines that can appear.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A large collection of hydrogen atoms is initially in the ground state. Each atom absorbs a photon of energy 12.09 eV, which excites it to the third Bohr orbit. The atoms are then allowed to de-excite through all possible paths. Find the maximum number of distinct emission lines that can appear.

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

G1 Physics · Accepted Answer

The absorbed energy 12.09 eV places the electron in the third orbit. For a large sample with levels n = 1, 2 and 3 available, every pair of levels can produce a distinct line. Number of distinct lines: N = 3×2 ÷ 2 = 3. Hence N = 3.