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AP Physics 2
15.3 Emission and Absorption Spectra
15.2 The Bohr Model of Atomic Structure
AdvancedMCQMathematicalConceptual13.2k
An energy level diagram showing four horizontal, parallel line segments representing atomic energy levels, vertically stacked. A vertical axis on the far left has an upward arrow labeled Energy (\(\text{eV}\)). The lowest horizontal line is labeled on the left with \(n = 1\) and on the right with \(-13.60 \text{ eV}\). The second line from the bottom is located above the first, labeled on the left with \(n = 2\) and on the right with \(-3.40 \text{ eV}\). The third line is positioned above the second line, closer to the second than the second is to the first, labeled on the left with \(n = 3\) and on the right with \(-1.51 \text{ eV}\). The fourth line is positioned above the third line, labeled on the left with \(n = 4\) and on the right with \(-0.85 \text{ eV}\). No other labels, lines, text, or axes appear.
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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