Chapter 40, Problem 1Q

To determine

To calculate:

(a) the number of sub-shells for n = 2

(b) the electron states n = 2

(c) the number of sub-shells for n = 5

(d) the electron states n = 5

Answer to Problem 1Q

Solution:

(a) For n = 2, it has 2 sub shells.

(b) For n = 2, there will be 8 electron states.

(c) For n = 5, it has 5 sub shells.

(d) For n = 5, there will be 50 electron states

Explanation of Solution

For a given quantum number n there are n possible values of l, ranging from 0 to n −1.

For each l the number of possible electron states with m_l values is (2l + 1).

For each m_l the electron can have two different spin orientations.

Thus, the total number of electron states for a given l is given by N_l = 2(2 l+ 1).

(e) For n = 2, it has 2 sub shells.

(f) For n = 2, the number of electrons 2n², there will be 8 electron states.

(g) For n = 5, it has 5 sub shells.

(h) For n = 5, the number of electrons 2n², there will be 50 electron states

Conclusion

For an l quantum number, there are (2l+1) number of possible m_l values.