To identify the compound repelled by an external magnetic field, we must evaluate the magnetic properties of each compound. Compounds are generally classified as diamagnetic or paramagnetic:
- Diamagnetic compounds possess no unpaired electrons and are thus repelled by a magnetic field.
- Paramagnetic compounds contain unpaired electrons and are attracted to a magnetic field.
The given options are analyzed as follows:
- \(\text{Na}_2[\text{CuCl}_4]\): The central atom, \(\text{Cu}^{2+}\), typically exhibits unpaired electrons, indicating paramagnetism.
- \(\text{K}_4[\text{Fe(CN)}_6]\): The central atom, \(\text{Fe}^{2+}\), is known to have unpaired electrons, classifying it as paramagnetic.
- \(\text{Na}_2[\text{CdCl}_4]\): The central atom is \(\text{Cd}^{2+}\). Cadmium in its common oxidation state generally lacks unpaired electrons, rendering it diamagnetic.
- \(\text{K}_3[\text{Fe(CN)}_6]\): The central atom, \(\text{Fe}^{3+}\), typically possesses unpaired electrons, classifying it as paramagnetic.
Consequently, \(\text{Na}_2[\text{CdCl}_4]\) is the compound that will be repelled by an external magnetic field due to its diamagnetic nature.