Multiple Choice
Which of the following best describes the qualitative features of a line spectrum produced by an excited hydrogen atom?
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9. Quantum Mechanics
Emission Spectrum
Multiple Choice
Which of the following transitions results in the emission of the highest-energy photon?
A
n = 2 → n = 5
B
n = 4 → n = 7
C
n = 7 → n = 4
D
n = 5 → n = 2
Verified step by step guidance1
Understand that the energy of a photon emitted during an electron transition is related to the difference in energy levels. The larger the difference, the higher the energy of the photon.
Recall that energy levels in an atom are quantized and are described by the principal quantum number, n. The energy difference between two levels is given by the formula: E = -13.6 eV * (1/n1^2 - 1/n2^2), where n1 and n2 are the initial and final energy levels, respectively.
For each transition, calculate the energy difference using the formula. For example, for the transition n = 7 to n = 4, substitute n1 = 7 and n2 = 4 into the formula.
Compare the calculated energy differences for each transition. The transition with the largest energy difference corresponds to the emission of the highest-energy photon.
Identify that the transition n = 5 to n = 2 has the largest energy difference, thus resulting in the emission of the highest-energy photon.
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