Multiple Choice
In which scenario will a woman observe a continuous rainbow of colors interrupted by a few dark absorption lines in the spectrum?
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9. Quantum Mechanics
Emission Spectrum
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Which of the following best describes the qualitative features of a line spectrum produced by an excited hydrogen atom?
A
It displays only a single line at one wavelength.
B
It consists of discrete lines at specific wavelengths corresponding to electronic transitions.
C
It shows a continuous range of colors without any gaps.
D
It contains lines that are evenly spaced across the entire visible spectrum.
Verified step by step guidance1
Understand that a line spectrum is produced when electrons in an atom transition between discrete energy levels, emitting photons of specific energies (and thus specific wavelengths).
Recall that the energy of the emitted photon corresponds to the difference between two energy levels, given by the formula \(\Delta E = E_{final} - E_{initial} = h \nu = \frac{hc}{\lambda}\), where \(h\) is Planck's constant, \(\nu\) is frequency, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
Recognize that because the energy levels in a hydrogen atom are quantized, only certain specific wavelengths (colors) of light are emitted, resulting in discrete lines rather than a continuous spectrum.
Note that these discrete lines correspond to electronic transitions between allowed energy levels, and their positions (wavelengths) can be predicted by the Rydberg formula for hydrogen: \(\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)\), where \(R\) is the Rydberg constant and \(n_1\) and \(n_2\) are integers with \(n_2 > n_1\).
Conclude that the qualitative feature of the hydrogen line spectrum is a set of discrete lines at specific wavelengths, each corresponding to a particular electronic transition, rather than a single line, a continuous spectrum, or evenly spaced lines.
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