How many molecules are in 0.610 moles of neon gas?

Consider hydrogen in an excited state n = 5n=5 that emits photons to reach the ground state. there are various possible transitions other than straight to the ground state that can occur; for example, it can drop to the n = 3n=3 state followed by the n = 3n=3 to the ground state transition. which of the possible transitions will result in the emission of a photon in the visible region?