When an electron makes a transition between energy levels of

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 . This rule is called a selection rule and states that = (+/-)1. In other words, when an electron makes a transition between energy levels, the value of can only increase or decrease by one. The value of may not remain the same or increase or decrease by more than one. According to this rule, which of the following energy level transitions are allowed: (a) 2s to 1s, (b) 2p to 1s, (c) 4p to 2p, (d) 4s to 2p, (e) 3d to 3s?

Solution

a. For energy level transitions 2s to 1s, the electron makes a transition from the 2s state (n=2,l=0) to the 1s state (n=1,l=0).since  the value of is the same in both states,i.e dl=0,Therefore this energy level transition is not allowed

b. For energy level transitions 2p to 1s, the electron makes a transition from the 2p state (n=2,l=1) to the 1s state (n=1,l=0).The value of l changes so that dL=0-1=-1.Therefore this energy level transition is allowed .

c.For energy level transitions 4 p to 2p, the electron makes a transition from the 4p state (n=4,l=1) to the 2p state (n=2,l=1).since  the value of is the same in both states,i.e dl=0,Therefore this energy level transition is not allowed .

d. For energy level transitions 4s to 2p, the electron makes a transition from the 4s state (n=4,l=0) to the 2p state (n=2,l=1).The value of l changes so that dL=1-0=1.Therefore this energy level transition is allowed.

e)For energy level transitions 3d to 3s, the electron makes a transition from the 3d state (n=3,l=2) to the 3s state (n=3,l=0).The value of l changes so that dL=0-2=-2.Therefore this energy level transition is not allowed.