i) hybridisation of Boron in - b) sp³

The EC of B is 1s² 2s² 2px¹ 2py⁰ 2pz⁰. In the excited state, one of the electrons from 2s orbitals gets shifted to a p-orbital. The tetrahedral geometry is formed when hybridisation occurs between one s and 3 p-orbitals to give sp³ hybridisation.

Here, in this case 3 molecules bind to the 3 orbitals of the Boron, but still the octet of the Boron is not yet completely filled. Therefore, an extra molecule of binds to it. Thereby involving one s-orbital and 3 p-orbitals in the hybridization process. Thus, it is hybridised.

ii) Aluminium in [Al(H₂O)₆]³⁺ - c) sp³d²

The EC of Al is 1s² 2s² 2px² 2py² 2pz² 3s² 3px¹. While in the excited state, one of the electrons from 2p and 3s orbitals gets shifted to 4s and 3d orbitals.

In other words, it can be said that in the excited state Al loses its 3 valence electrons (from the s and p-orbitals of the valence shell). Now, it accepts 6 electron pairs from water molecule and extended its orbital to d. Thus, forming sp³d² hybridisation.

iii) Boron in - b) sp³

The EC of B is 1s² 2s² 2px¹ 2py⁰ 2pz⁰. In the excited state, one of the electrons from 2s orbitals gets shifted to a p-orbital. When hybridisation occurs between one s and 3 p-orbitals it gives sp³ hybridisation.

Normal state EC of B: 1s² 2s² 2px¹ 2py⁰ 2pz⁰

Here, in this case 3 molecules bind to the 3 orbitals of one Boron. Similarly, 3 hydrogen ions are bonded with another Boron atom by making 1 s- and 3 p- orbitals. Thereby involving one s-orbital and 3 p-orbitals in the hybridization process in each case. Thus, it is hybridised.

iv) Carbon in Buckminsterfullerene – a) sp²

In this case, each carbon atom is sp² hybridised while the remaining p- orbital available for bonding binds with another C-atom with sp² hybridisation.

Normal state EC of C: 1s² 2s² 2px² 2py⁰ 2pz⁰

In the case of Buckminsterfullerene, it is composed of 60 atoms of carbon (allotrope of Carbon), here, the hydrogen atoms hybridize with Carbon atoms while, the last p-orbital participates in hybridisation with the adjacent Carbon atoms. Thus, sp² hybridisation.

v) Silicon in SiO^4-₄ - b) sp³

The EC of Si is 1s² 2s² 2p⁶ 3s² 3p². In the excited state, one of the electrons from 3s and 3p orbitals gets shifted to a p-orbitals. When hybridisation occurs between one s and 3 p-orbitals it gives sp³ hybridisation.

Normal state EC of Si: 1s² 2s² 2p⁶ 3s² 3p²

In this case, due to the presence of vacant d-orbitals Si extends its coordination number and forms bonding and accommodates four atoms of oxygen.

(vi) Germanium in [GeCl₆]^2-- c) sp³d²

The EC of Ge = [Ar] 3d¹⁰ 4s² 4p² 4d⁰

EC of Ge (IV) [Ar] 3d¹⁰ 4s⁰ 4p⁰ 4d⁰

Now, 6 Cl atoms donate 6 lone pairs of electrons to Ge which gets accommodated in 1 4s orbitals, 3 4p orbitalswhile the remaining 2 Cl atoms gets into the 4d orbitals thereby forming sp³d² hybridisation.