Checking units of each option:

$\mu=\frac{ e ^{2} c }{\text { ha }} \Rightarrow=\frac{\text { Coulomb }^{2} ms ^{-1}}{ kgm ^{2} s ^{-1} m }= C ^{2} kg ^{-1} m ^{-2} s ^{0}$

$\mu=\frac{ e ^{2} h }{ ca _{\circ}} \Rightarrow=\frac{\text { Coulomb }^{2} kgm ^{2} s ^{-1}}{ ms ^{-1} m }= C ^{2} kg ^{1} m ^{0} s ^{0}$

$\mu=\frac{\text { hc }}{ e ^{2} a _{\circ}} \Rightarrow=\frac{ kgm ^{2} s ^{-1} ms ^{-1}}{\text { Coulomb }^{2} m }= C ^{-2} kg ^{1} m ^{1} s ^{-2}$

$\mu=\frac{ e ^{2} a _{\circ}}{ hc } \Rightarrow=\frac{\text { Coulomb }^{2} m }{ kgm ^{2} s ^{-1} ms ^{-1}}= C ^{2} kg ^{-1} m ^{-2} s ^{-2}$