Physics

Physics

Problem

A simplified energy-level diagram for an atom has the following energies (in eV): E4=0.0E_4 = 0.0, E3=−1.5E_3 = -1.5, E2=−3.0E_2 = -3.0, and E1=−5.0E_1 = -5.0. Which electronic transition would produce the photon with the shortest wavelength? a) E4→E3E_4 \to E_3 b) E3→E1E_3 \to E_1 c) E4→E2E_4 \to E_2 d) E1→E3E_1 \to E_3
Intuitive explanation

The shortest wavelength corresponds to the highest energy photon, so you need to find which transition releases the most energy. The energy released in a transition is the difference between two levels: ΔE=Einitial−Efinal\Delta E = E_{\text{initial}} - E_{\text{final}}. Since electrons fall from higher (less negative) to lower (more negative) levels, look for the pair of levels with the largest energy gap—that's your answer.

Intuitive explanation

The shortest wavelength corresponds to the highest energy photon, so you need to find which transition releases the most energy. The energy released in a transition is the difference between two levels: ΔE=Einitial−Efinal\Delta E = E_{\text{initial}} - E_{\text{final}}. Since electrons fall from higher (less negative) to lower (more negative) levels, look for the pair of levels with the largest energy gap—that's your answer.

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