Q.Why the ground-state electronic configurations of gadolinium and lawrentium are different than expected?

Step 1. Gadolinium's expected vs observed configuration. Following the simple lanthanoid filling pattern (continuing to add 4f electrons after europium's 4f7), the naively-expected configuration for gadolinium (Z=64) would be [Xe] 4f8 6s2. The OBSERVED configuration, given in Table 8.11, is instead [Xe] 4f7 5d1 6s2 -- one electron sits in 5d rather than continuing to fill 4f.

Step 2. Why gadolinium departs from the expected pattern. Placing that extra electron in 5d instead of 4f leaves the 4f subshell at exactly 4f7 -- a HALF-FILLED subshell, which carries extra stability (the same principle behind chromium's 3d5 4s1 configuration, Section 8.3.1) -- while adding a single 5d electron. Because 4f and 5d are extremely close in energy for the lanthanoids (Section 8.12.1), this small extra stability from a half-filled 4f7 is enough to favour the 4f7 5d1 configuration over the naive 4f8.

Step 3. Lawrencium's expected vs observed configuration. Following the analogous actinoid filling pattern (continuing to add 5f electrons after nobelium's 5f14, since No is already full), a naive continuation might expect lawrencium (Z=103) to simply add its extra electron to 7p or elsewhere; the OBSERVED configuration, given in Table 8.14, is [Rn] 5f14 6d1 7s2 -- placing the extra electron in 6d while keeping the 5f subshell exactly full at 5f14. …

Comparing Table 8.11/8.14's observed configurations against the naively-expected continuation of each series' filling pattern, applying the chapter's …

• Explaining only one of the two elements (Gd or Lr) when the question asks about both.
• Missing that this is the SAME underlying principle (half-filled/fully-filled extra stability) already used for Cr/C …