Which electronic transition in a hydrogen atom corresponds to the lowest energy?

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

Answer: (A)

Verified step by step guidance

1. Recall that the energy of an electronic transition in a hydrogen atom is given by the difference in energy levels, which can be calculated using the formula: \(\Delta E = -13.6 \left( \frac{1}{{n_f}^2} - \frac{1}{{n_i}^2} \right)\) eV, where \(n_i\) is the initial energy level and \(n_f\) is the final energy level.
2. Understand that the energy difference \(\Delta E\) corresponds to the energy of the photon absorbed or emitted during the transition, and the magnitude of \(\Delta E\) determines the energy of the transition (larger \(\Delta E\) means higher energy).
3. Calculate the absolute value of \(\Delta E\) for each given transition: from \(n=4\) to \(n=3\), \(n=2\) to \(n=1\), \(n=3\) to \(n=2\), and \(n=5\) to \(n=2\) using the formula above.
4. Compare the calculated energy differences for all transitions to identify which one has the smallest energy difference, as this corresponds to the lowest energy transition.
5. Conclude that the transition with the smallest \(\Delta E\) value corresponds to the lowest energy electronic transition in the hydrogen atom.