Multiple Choice
Calculate the wavelength (in nm) of the blue light emitted by a mercury lamp with a frequency of 6.32 × 10^14 Hz. (Use the speed of light, c = 3.00 × 10^8 m/s)
9. Quantum Mechanics
Wavelength and Frequency
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Which of the following transitions requires the absorption of the most energetic photon?
A
Transition I: n = 2 → n = 3
B
Transition III: n = 3 → n = 4
C
Transition V: n = 2 → n = 2
Verified step by step guidance1
Understand that the energy of a photon absorbed or emitted during an electronic transition in a hydrogen atom is given by the formula: E = -13.6 eV * (1/n_final^2 - 1/n_initial^2), where n_initial and n_final are the principal quantum numbers of the initial and final states, respectively.
Recognize that the transition requiring the absorption of the most energetic photon will have the largest positive change in energy (E).
Calculate the energy change for Transition I: n = 2 → n = 3 using the formula: E = -13.6 eV * (1/3^2 - 1/2^2).
Calculate the energy change for Transition III: n = 3 → n = 4 using the formula: E = -13.6 eV * (1/4^2 - 1/3^2).
Compare the calculated energy changes for each transition. The transition with the largest positive energy change corresponds to the absorption of the most energetic photon.
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