# Consider just four of the energy levels in a certain atom,...

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smith (svs473) – Ch8-H2 – turner – (56970) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points Consider just four of the energy levels in a certain atom, as shown in the diagram below. n = 1 n = 2 n = 3 n = 4 How many spectral lines will result from all possible transitions among these levels? Which transition corresponds to the highest- frequency light emitted? Which transition corresponds to the lowest-frequency? n = 1 The highest-frequency transition is from quantum level 4 to level 1. The lowest- frequency transition is from quantum level 4 to level 3. 002 (part 2 of 3) 10.0 points An electron de-excites from the fourth quan- tum level to the third and then directly to the ground state. Two photons are emitted. How does the sum of their frequencies com- pare to the frequency of the single photon that would be emitted by de-excitation from the fourth level directly to the ground state? 1. six; level 4 to level 1 transition; level 4 to level 3 transition. correct 2. three; level 4 to level 1 transition; level 4 to level 3 transition. 3. three; level 2 to level 1 transition; level 4 to level 3 transition. 4. three; level 4 to level 3 transition; level 2 to level 1 transition. Explanation: Six transitions are possible, as shown. 1. None of these 2. The sum is equal to the frequency of the single photon. correct 3. The sum is smaller than the frequency of the single photon. 4. The sum is larger than the frequency of the single photon. Explanation: As shown in the diagram, the sum of the two frequencies is equal to the frequency of light emitted in the transition from quantum level 4 to the ground state, quantum level 1. Because energies are additive, so are the frequencies. However, the wavelength rela- tionship is not that simple: wavelength is in- versely proportional to the frequency, so the reciprocals of the wavelengths are additive: 1 λ 4 3 + 1 λ 3 1 = 1 λ 4 1 n = 2 n = 3 n = 4
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