In a hydrogen atom, which electron transition would emit the longest wavelength of light?

• A. n = 3 to n = 2
• B. n = 2 to n = 1
• C. n = 5 to n = 1
• D. n = 4 to n = 2

Answer: (A)

Verified step by step guidance

1. Recall that the wavelength of light emitted during an electron transition in a hydrogen atom is related to the energy difference between the two energy levels involved. The energy of a photon emitted corresponds to the difference in energy between the initial and final states.
2. Use the Rydberg formula for the wavelength of emitted light during an electron transition: \[ \frac{1}{\lambda} = R \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \] where \(\lambda\) is the wavelength, \(R\) is the Rydberg constant, \(n_i\) is the initial energy level, and \(n_f\) is the final energy level.
3. Understand that a smaller energy difference between levels corresponds to a smaller value of \(\frac{1}{\lambda}\), which means a longer wavelength \(\lambda\) (since wavelength and energy are inversely related).
4. Calculate or compare the values of \(\left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right)\) for each transition given: - \(n=3\) to \(n=2\) - \(n=2\) to \(n=1\) - \(n=5\) to \(n=1\) - \(n=4\) to \(n=2\) The transition with the smallest difference will emit the longest wavelength.
5. Identify that the transition from \(n=3\) to \(n=2\) has the smallest energy difference among the options, and therefore it emits the longest wavelength of light.