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6 Electronic Structure of Atoms Solutions to Exercises (c) The square of the wave function has the physical significance of an amplitude, or probability. The quantity at a given point in space is the probability of locating the electron within a small volume element around that point at any given instant. The total probability, that is, the sum of over all the space around the nucleus, must equal 1. 6.51 (a) The possible values of are 1) to 0. n = 4, = 3, 2, 1, 0 (b) The possible values of are to +1. = 2, = -2, -1, 0, 1, 2 (c) Since the value of is less than or equal to the value of 1, = 2 must have an 1- value greater than or equal to 2. In terms of elements that have been observed, the possibilities are 2, 3 and 4. 6.52 (a) For n = 3, there are three values (2, 1, 0) and nine values = 2; II (b) For n = 5, there are five values (4,3,2,1,0) and twenty-five m, values = 4, = -4 to +4; = 3, m, = -3 to +3; = 2, = -2 to +2; = 1, = -1 to +1; = 0, = 0). In general, for each principal quantum number n there are n and n² For each shell, there are n kinds of orbitals and n² total orbitals. 6.53 (a) (b) 2s: n = 2, = 0 (c) (d) 5d: n = 5, = 2 6.54 (a) 2,1,1; 2, 1, 0; 2,1, -1 (b) 5,2,2; 5, 2, 1; 5, 2, 0; 5,2, -1; 5,2,-2 6.55 Impossible: (a) 1p, only 1=0 is possible for n = 1; (d) 2d, for n = 2, = 1 or 0, but not 2 6.56 n orbital 2 1 -1 2p (example) 1 0 0 1s 3 -3 2 not allowed