When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number n. According to quantum mechanics, however, there is a rule that restricts the initial and final values of the orbital quantum number ℓ. This rule is called a selection rule and states that ∆ℓ = ± 1. In other words, when an electron makes a transition between energy levels, the value of ℓ can only increase or decrease by one. The value of ℓ may not remain the same nor may it increase or decrease by more than one. According to this rule, which of the following energy level transitions are allowed?

(a) 2s → 1s

(b) 2p → 1s

(c) 4p → 2p

(d) 4s → 2p

(e) 3d → 3s