An electron in a hydrogen atom transitions from the \(n = 3\) energy level to the \(n = 1\) ground state, emitting a photon with energy \(E_1\). In a separate process, an electron in a hydrogen atom transitions from the \(n = 3\) level to the \(n = 2\) level, emitting a photon with energy \(E_2\). What is the ratio \(\dfrac{E_1}{E_2}\)?