Gadolinium belong A. [Xe] 4f⁷5d¹6s²

B. [Xe] 4f⁶5d²6s²

C. [Xe] 4f⁸6d²

D. [Xe] 4f⁹5s¹

Here, according to Aufbau principle electron should enter 6s, 4f and then 5d,

n+l rule for

4f= 4+3 =7

5d= 5+2=7

6s= 6+0=6

Atomic number of xenon is 54, the remaining 10 electrons are distributed into 4f, 5d and 6s. Only 7 electrons go into 4f because half filled orbital leads to stability. Now, the remaining 3 electrons, two of them go into 6s and one goes into 5d.