Answer:

Introduction:
Spin-only magnetic moment is the magnetic moment of a coordination compound that arises due to the net spin of the unpaired electrons present in the d-orbitals of the central metal ion.

Explanation:
The spin-only magnetic moment of a coordination compound can be calculated using the following formula:

µS = √n(n+2)BM

where, n is the number of unpaired electrons and BM is the Bohr magneton.

(a) d⅝5 (in strong ligand field):
The number of unpaired electrons in d⅝5 is 5. In strong ligand field, the pairing of electrons takes place and hence, the number of unpaired electrons decreases. Therefore, the spin-only magnetic moment of d⅝5 in strong ligand field will be less than 2.84 BM. Hence, option (a) is not correct.

(b) d³ (in weak as well as in strong fields):
The number of unpaired electrons in d³ is 3. The spin-only magnetic moment of d³ in weak field is given by:

µS = √3(3+2)BM = 3.87 BM

In strong field, the pairing of electrons takes place and hence, the number of unpaired electrons decreases. Therefore, the spin-only magnetic moment of d³ in strong ligand field will be less than 3.87 BM. Hence, option (b) is not correct.

(c) d⁴ (in weak ligand fields):
The number of unpaired electrons in d⁴ is 2. The spin-only magnetic moment of d⁴ in weak field is given by:

µS = √2(2+2)BM = 2.83 BM

This value is close to 2.84 BM. Therefore, option (c) can be considered as correct.

(d) d⁴ (in strong ligand fields):
In strong ligand field, the pairing of electrons takes place and hence, the number of unpaired electrons decreases. Therefore, the spin-only magnetic moment of d⁴ in strong ligand field will be less than 2.83 BM. Hence, option (d) is not correct.

Conclusion:
Hence, the correct option is (c) d⁴ (in weak ligand fields).