In an anti-bonding MO the electron density is minimum

between the nuclei

The correct answer is option 2. between the nuclei.

Let us delve into the explanation of electron density in anti-bonding molecular orbitals (MOs):

Anti-bonding molecular orbitals (MOs) are formed when atomic orbitals of similar energy combine with phases that are out of phase (i.e., with opposite signs). This results in a nodal plane or nodal region between the nuclei of the atoms involved in bonding. Here’s a detailed explanation:

Formation of Anti-bonding MOs:

When atomic orbitals combine in an anti-phase manner (one positive and one negative lobes overlap), they form an anti-bonding molecular orbital. In this scenario, the phases of the atomic orbitals interfere destructively. This means that where one orbital has an electron density, the other has a node (where electron density is zero).

Location of Electron Density:

In an anti-bonding MO, the electron density is minimized or reduced specifically between the nuclei of the bonded atoms. This region of low electron density is due to the presence of a nodal plane or nodal region where the wavefunctions of the atomic orbitals cancel each other out.

Significance of the Nodal Plane:

The nodal plane is where the probability of finding electrons is zero. This is because the phases of the atomic orbitals cancel each other out at this point. This characteristic of anti-bonding MOs contrasts with bonding MOs, where the electron density is concentrated between the nuclei, promoting bonding.

Answer Clarification:

Option (2) "between the nuclei" correctly describes the location of minimum electron density in an anti-bonding MO. This is because the nodal plane exists precisely between the nuclei of the atoms forming the bond.

Therefore, the correct answer remains: (2) between the nuclei

This explanation should clarify why this option accurately describes the electron density distribution in an anti-bonding molecular orbital.