Sm
For an element to have a partially filled f orbital, it will have to have an f orbital in the first place, this cancels barium, as it is the lightest of the elements listed:
Barium does not have an f orbital:
[Xe]6s^2
or
1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^10 4p^6 5s^2 4d^10 5p^6 6s^2
Sm:
[Xe] 4f6 6s2
Does have an f orbital AND they are partially filled (the F subshell has the potential to hold 14 electrons, but Sm only holds 6 electrons on its F subshell, therefore the electrons, by the rule of maximum multiplicity, in which the electrons will try to occupy orbitals by themselves first (the F subshell has 7 orbitals because 14/2 = 7), it leaves the f subshell with partially filled orbitals.
Os:
Xe 4f14 5d6 6s2
all occupied f orbitals
Bi:
Xe 4f14 5d10 6s2 6p3
Has full F orbitals