Gadolinium is an element, number 64 on the periodic table.
Spock's memory test taken in 2286 asked him to specify the electron configuration of gadolinium. (Star Trek IV: The Voyage Home)
According to the script, his answer was 5s22s22p63d104s24p64d104f75s25p64d16s2.
Gadolinium at Wikipedia shows the electron configuration of Gadolinium as "1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 5s² 5p⁶ 4f⁷ 5d¹ 6s²". In Spock's script answer (expanded to be more readable as "5s² 2s² 2p⁶ 3d¹⁰ 4s² 4p⁶ 4d¹⁰ 4f⁷ 5s² 5p⁶ 4d¹ 6s²") the 4d¹⁰ orbital is listed correctly with 10 electrons. However, the end sequence "4d¹ 6s²" in the script should have been "5d¹ 6s²". The script answer lists orbitals out of sequence (begins with "5s²") and is also missing the 1s², 3s², 3p⁶ orbitals.
For the majority of stars, the rare element europium was enriched relative to gadolinium and samarium. (TNG: "Manhunt")
In reality, europium is less abundant than both samarium and gadolinium in both Sol and throughout the universe, indicating that this is not the case for most stars.