PHYS212-071
HW # 10 Solutions (Chapter 8)
(Numbers refer to 2nd Edition of Textbook)
3. How many different sets of quantum numbers are possible for an electron for which (a)
n = 1, (b) n = 2, (c) n = 3, (d) n = 4, and (e) n = 5? Check your results to show that they
agree with the general rule that the number of different sets of quantum numbers is equal
to 2n2.
(a) n = 1, l = 0, ml = 0, ms = 1/2, +1/2,
Total of 2 states, 212 = 2
(b) n = 2, l = 0, ml = 0, ms = 1/2, +1/2
l = 1, ml =  1, 0, + 1, ms = 1/2, +1/2
Total of 2 + 6 = 8 states, 222 = 8
(c) n = 3, l = 0, ml = 0, ms = -1/2, +1/2
l = 1, ml =  1, 0, + 1, ms = 1/2, +1/2
l = 2, ml =  2,  1, 0, + 1, + 2, ms = 1/2, +1/2
Total of 2 + 6 +10 = 18 states, 232 = 18
(d) n = 4, l = 0, ml = 0
l = 1, ml = 1, 0, + 1, ms = -1/2, + 1/2
l = 2, ml =  2,  1, 0, + 1, + 2, ms = 1/2, +1/2
l = 3, ml =  3,  2,  1, 0, + 1, + 2, + 3, ms = 1/2, +1/2
Total of 2 + 6 + 10 + 14 = 32 states, 242 = 32
(e) n = 5, l = 0, ms = 1/2, +1/2
l = 1, ml =  1, 0, + 1, ms = 1/2, +1/2
l = 2, ml =  2,  1, 0, + 1, + 2, ms = 1/2, +1/2
l = 3, ml =  3,  2,  1, 0,  1, + 2, + 3, ms = 1/2, +1/2
l = 4, ml =  4,  3,  2,  1, 0, +1, +2, +3, +4, ms = 1/2, +1/2
Total of 2 + 6 +10 + 14 +18 = 50 states, 252 = 50
10. Consider a single-electron atom in the n = 2 state. Find all possible values for j and mj
for this state.
n = 2, l =0, j = 1/2, mj = 1/2, +1/2
l = 1, j = 1/2, mj = 1/2, +1/2
j = 3/2, mj = 3/2, 1/2, +1/2, +3/2
11. Find all possible values of j and mj for a d electron.
l = 2, j = 3/2, mj = 3/2, 1/2, +1/2, +3/2
j = 5/2, mj = 5/2, 3/2, 1/2, +1/2, +3/2, +5/2
12. Give the spectroscopic notation for the following states:
(a) n = 7, l = 4, j = 9/2; (b) all the possible states of an electron with n = 6 and l = 5.
(a) 7G9/2
(b) 6H9/2, 6H11/2
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