A substance is repelled by an external magnetic field if it is diamagnetic. Diamagnetism arises from the absence of unpaired electrons in the atoms or ions making up the substance. Conversely, substances with unpaired electrons are paramagnetic and are attracted to a magnetic field.

Identifying Repelled Compounds

To find the compounds repelled by a magnetic field, we need to identify which ones are diamagnetic by examining the electronic configuration of their central metal ions.

Compound Analysis:

• 1. $Na_2[CuCl_4]$
  • Central Ion: $Cu^{2+}$
  • Electronic Configuration: $Cu$ is $[Ar] 3d^{10} 4s^1$. $Cu^{2+}$ is $[Ar] 3d^9$.
  • Unpaired Electrons: There is 1 unpaired electron in the $3d$ orbital.
  • Magnetic Property: Paramagnetic (Attracted).
• 2. $Na_2[CdCl_4]$
  • Central Ion: $Cd^{2+}$
  • Electronic Configuration: $Cd$ is $[Kr] 4d^{10} 5s^2$. $Cd^{2+}$ is $[Kr] 4d^{10}$.
  • Unpaired Electrons: There are 0 unpaired electrons.
  • Magnetic Property: Diamagnetic (Repelled).
• 3. $K_4[Fe(CN)_6]$
  • Central Ion: $Fe^{2+}$
  • Electronic Configuration: $Fe$ is $[Ar] 3d^6 4s^2$. $Fe^{2+}$ is $[Ar] 3d^6$.
  • Ligand Effect: Cyanide ($CN^-$) is a strong field ligand. For $d^6$ configuration with a strong ligand, the electrons pair up (low spin state).
  • Unpaired Electrons: 0 unpaired electrons ($t_{2g}^6$).
  • Magnetic Property: Diamagnetic (Repelled).
• 4. $K_3[Fe(CN)_6]$
  • Central Ion: $Fe^{3+}$
  • Electronic Configuration: $Fe$ is $[Ar] 3d^6 4s^2$. $Fe^{3+}$ is $[Ar] 3d^5$.
  • Ligand Effect: Cyanide ($CN^-$) is a strong field ligand. For $d^5$ configuration with a strong ligand, electrons pair up as much as possible (low spin state).
  • Unpaired Electrons: There is 1 unpaired electron ($t_{2g}^5$).
  • Magnetic Property: Paramagnetic (Attracted).

Conclusion

The compounds $Na_2[CdCl_4]$ and $K_4[Fe(CN)_6]$ are diamagnetic because their central metal ions ($Cd^{2+}$ and $Fe^{2+}$, respectively) have no unpaired electrons in their d-orbitals under the influence of the cyanide ligand in the latter case. Therefore, these compounds will be repelled when placed in an external magnetic field.