Which of the following elements have half-filled f-orbitals in...

f-subshell contains seven orbitals in it. Hence, if seven electrons are present in these orbitals then it said to be half-filled. Electronic configuration of all the elements are:

$Sm ( Z = 62 ) = 4{f}^{6}{s}^{2}$

$Eu ( Z = 63 ) = 4{f}^{7}6{S}_{2}$

$Tb ( Z = 65 ) = 4{f}^{9}6{s}^{2}$

$Gd ( Z = 64 ) = 4{f}^{7}5{d}^{1}6{s}^{2}$

$Pm ( Z = 61 ) = 4{f}^{5}6{s}^{2}$

So, $Eu$ & $Gd$ have half-filled configuration.