Multiple Choice
Which of the following electronic transitions in a hydrogen atom represents the emission of a photon with the largest energy?
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9. Quantum Mechanics
The Energy of Light
Multiple Choice
Which of the following frequencies of light has the highest energy?
A
1.0 × 10^{15} Hz
B
8.0 × 10^{13} Hz
C
5.0 × 10^{14} Hz
D
2.0 × 10^{14} Hz
Verified step by step guidance1
Recall the relationship between the energy of a photon and its frequency, which is given by the equation \(E = h \times f\), where \(E\) is the energy, \(h\) is Planck's constant, and \(f\) is the frequency of the light.
Understand that Planck's constant \(h\) is a fixed value (\(6.626 \times 10^{-34}\) J·s), so the energy of a photon is directly proportional to its frequency.
Compare the given frequencies: \(8.0 \times 10^{13}\) Hz, \(5.0 \times 10^{14}\) Hz, \(2.0 \times 10^{14}\) Hz, and \(1.0 \times 10^{15}\) Hz.
Identify the highest frequency among the options, since the highest frequency corresponds to the highest energy according to the direct proportionality.
Conclude that the frequency \(1.0 \times 10^{15}\) Hz has the highest energy because it is the largest frequency value given.
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