Which one of the following species doesn't have a magnetic moment of 1.73 BM, (spin only value)?

A magnetic moment of 1.73 BM corresponds to spin-only value for one unpaired electron, since $$\mu = \sqrt{n(n+2)} = \sqrt{1 \times 3} = \sqrt{3} \approx 1.73$$ BM.

For $$O_2^+$$: molecular orbital configuration removes one electron from $$O_2$$. $$O_2$$ has 2 unpaired electrons; $$O_2^+$$ has 1 unpaired electron. So $$\mu = 1.73$$ BM. ✓

For $$O_2^-$$: adds one electron to $$O_2$$. This gives 1 unpaired electron (the extra electron pairs up one of the $$\pi^*$$ electrons). So $$\mu = 1.73$$ BM. ✓

For $$[\text{Cu(NH}_3)_4]Cl_2$$: here Cu is in +2 state (Cu²⁺). Cu²⁺ has configuration [Ar]$$3d^9$$, with 1 unpaired electron. So $$\mu = 1.73$$ BM. ✓

For CuI: here Cu is in +1 state (Cu⁺). Cu⁺ has configuration [Ar]$$3d^{10}$$, which is completely filled with no unpaired electrons. Therefore $$\mu = 0$$ BM, not 1.73 BM.

CuI does not have a magnetic moment of 1.73 BM.