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AP Physics 2
15.3 Emission and Absorption Spectra
15.2 The Bohr Model of Atomic Structure
AdvancedMCQMathematicalConceptual13.2k
Energy levels of the hydrogen atom for n = 1 to n = 4.
Energy levels of the hydrogen atom for n = 1 to n = 4.
A gas discharge tube contains a large sample of isolated hydrogen atoms whose electrons are all excited to the \(n = 4\) energy level. The energy levels of the hydrogen atom are given by \(E_n = -\dfrac{13.6 \text{ eV}}{n^2}\), and visible light corresponds to photon energies between \(1.8 \text{ eV}\) and \(3.1 \text{ eV}\). The electrons de-excite to the ground state (\(n = 1\)) through all possible direct and multi-step cascade pathways.

OptionPhotons in \(n = 4 \to 3 \to 1\) CascadePhotons in \(n = 4 \to 2 \to 1\) CascadeDistinct Visible Lines from Sample
(A)One visible, one ultravioletTwo ultraviolet1
(B)Two ultravioletOne visible, one ultraviolet3
(C)One infrared, one visibleOne visible, one ultraviolet2
(D)One infrared, one ultravioletOne visible, one ultraviolet2

Which row in the table correctly classifies the spectral regions of the emitted photons for the two cascade pathways and gives the total number of distinct visible-light wavelengths emitted by the sample?

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