Gadolinium (atomic number 64) belongs to the 4f series.
The correct electronic configuration of gadolinium among the following is:

\(1. (X e) 4 f^{7} 5 d^{1} 6 s^{2} \)

2. \( (X e) 4 f^{6} 5 d^{2} 6 s^{2}\)

3. \((X e) 4 f^{8} 6 d^{2}\)

4. \((X e) 4 f^{9} 5 s^{1}\)

Hint:  To maintain the half-filled subshell in 4f, the next electron transfer is the 5d subshell. 
Gadolinium belongs to the 4f series and has the atomic number 64. The correct electronic configuration of gadolinium is 
Xe 4f7 5d1 6s2 It has extra stability due to the half-filled 4f subshell.