The number of states in the He⁺ ion corresponding to the principle quantum number n = 5 are A) 18 B) 25 C) 50 D) 9 E) 11

Question

Quizplus · Accepted Answer

For the HeS1U1P1 term, there are (2S+1)(2L+1) states where S and L are the total spin and orbital angular momentum quantum numbers, respectively. For n=5, L can range from 0 to 4 (since L<n), and there are 2S+1=2 states for each value of L. So for HeS1U1P1, there are (2+1)(2(0)+1)+(2+1)(2(1)+1)+(2+1)(2(2)+1)+(2+1)(2(3)+1)+(2+1)(2(4)+1) = 3+15+35+63+99 = 215 states.

For the S1S1P0 term, the parity is even (since L=0 for P0), so there is only one state.

Therefore, the total number of states is 215*1 = 215, which corresponds to choice C.

The Number of States in the He+ Ion Corresponding to the Principle

The Number of States in the He⁺ Ion Corresponding to the Principle