A large collection of ground-state hydrogen atoms absorbs monochromatic photons of energy 12.75 eV, exciting the electrons to the fourth Bohr orbit. The atoms subsequently de-excite through all possible paths. Find the maximum number of distinct emitted wavelengths.
Physics · Atomic Structure and X-rays · atomic structure and bohr atomic model
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Question

A large collection of ground-state hydrogen atoms absorbs monochromatic photons of energy 12.75 eV, exciting the electrons to the fourth Bohr orbit. The atoms subsequently de-excite through all possible paths. Find the maximum number of distinct emitted wavelengths.

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

G1 Physics · Accepted Answer

An absorbed energy of 12.75 eV takes a hydrogen atom from the ground state to the fourth orbit. For a large sample with four participating levels, the number of distinct transitions is N = 4×3 ÷ 2 = 6. Each transition has a distinct energy and therefore a distinct wavelength. Hence N = 6.