Match List I with List II

Choose the correct answer from the options given below:

A-III, B-I, C-IV, D-II

The correct answer is option 2. A-III, B-I, C-IV, D-II.

(A) Ferrimagnetic : (III) \(ZnFe_2O_4\):

Ferrimagnetic materials are a type of magnetic material where the magnetic moments of the ions in the material are aligned in opposite directions, but the opposing moments are unequal, resulting in a net magnetic moment.

In the case of \(ZnFe_2O_4\), which is zinc ferrite, the material exhibits ferrimagnetism. This is because the iron ions in the ferrite are distributed between two types of sites: tetrahedral and octahedral. The magnetic moments of the iron ions in these sites align in opposite directions, but the moments are not equal, resulting in a net magnetic moment and thus ferrimagnetism.

So, (A) Ferrimagnetic corresponds to (III) \(ZnFe_2O_4\).

(B) Antiferromagnetic : (I) \(MnO\) :

Antiferromagnetism is a type of magnetic ordering where the magnetic moments of adjacent ions or atoms align in opposite directions. This antiparallel alignment cancels out the overall magnetic moment, leading to no net macroscopic magnetization in the material.

\(MnO\) has a rock-salt (NaCl) structure where manganese ions (Mn\(^{2+}\)) are in an octahedral coordination with oxygen ions. The manganese ions have a \(d^5\) electronic configuration, which results in a high spin state. In the high spin state, the magnetic moments of the Mn\(^{2+}\) ions align in such a way that adjacent manganese ions have their magnetic moments pointing in opposite directions.

The magnetic moments of adjacent Mn\(^{2+}\) ions align antiparallel to each other due to superexchange interactions mediated by the oxygen ions. This antiparallel alignment of the magnetic moments results in a cancellation of the overall magnetic moment of the material, which is characteristic of antiferromagnetism.

In summary, \(MnO\) is antiferromagnetic because the magnetic moments of the manganese ions align in opposite directions, resulting in no net magnetization. This behavior is typical of materials with antiferromagnetic ordering.

(C) Ferrimagnetic  : (IV) \(CrO_2\) :

Ferrimagnetism is a type of magnetic ordering where the magnetic moments of different ions or atoms are aligned in opposite directions but with unequal magnitudes. This results in a net macroscopic magnetization because the opposing moments are not equal.

\(CrO_2\) has a rutile structure where chromium ions (Cr\(^{4+}\)) are in a distorted octahedral coordination with oxygen ions. The chromium ions have a high-spin \(d^3\) electronic configuration, leading to magnetic ordering.

In \(CrO_2\), the chromium ions contribute to magnetic moments that are aligned in opposite directions within different sublattices. The unequal alignment of magnetic moments in these sublattices results in a net magnetization, characteristic of ferrimagnetism.

Thus, (C) Ferrimagnetic corresponds to (IV) \(CrO_2\), as \(CrO_2\) exhibits ferrimagnetic behavior with a net magnetic moment due to the unequal opposing alignments of magnetic moments in different sublattices.

(D) Diamagnetic : (II) \(H_2O\) :

Diamagnetic materials are characterized by their ability to create an induced magnetic field in opposition to an external magnetic field, resulting in a net repulsion from the magnetic field. This is due to the paired electrons in these materials.

Diamagnetic materials do not have any permanent magnetic moments. Instead, they exhibit diamagnetism due to the rearrangement of electron orbits in response to an external magnetic field. This results in a slight repulsion from the external magnetic field, which is generally very weak compared to other types of magnetism.

Water (\(H_2O\)) has a molecular structure where the electrons in the oxygen and hydrogen atoms are paired. In the presence of an external magnetic field, the electron orbits in water adjust slightly to oppose the field, resulting in a diamagnetic response. Water is a diamagnetic substance because it does not have any unpaired electrons and thus does not have a net magnetic moment.

So, (D) Diamagnetic corresponds to (II) \(H_2O\) because water is diamagnetic due to the paired nature of its electrons, leading to a weak repulsion from external magnetic fields.