Animated Solution for Chemistry - s and p-Block Elements: The type of hybridisation of boron in diborane is

Diborane ($B_2{H}_6$) is one of those fascinating molecules in chemistry that forces us to rethink our basic understanding of chemical bonding. At first glance, if you try to draw a Lewis structure for $B_2{H}_6$, you will quickly run into a wall. Boron is a Group 13 element, meaning it has only 3 valence electrons. Two boron atoms give us 6 electrons, and six hydrogen atoms give us another 6. That's a total of 12 valence electrons.

However, to form a standard ethane-like structure ($H_{3}B-B{H}_3$), we would need 7 bonds (6 B-H bonds and 1 B-B bond), which requires 14 electrons! This shortage of electrons is why diborane is famously known as an electron-deficient compound.

Nature always finds a way to achieve stability. Since there aren't enough electrons to form normal 2-center-2-electron ($2c-2e$) bonds everywhere, diborane adopts a unique bridged structure.

Imagine the two Boron atoms at the center. Four of the six Hydrogen atoms form normal, covalent $2c-2e$ bonds with the Boron atoms. These are called the terminal hydrogens. They sit on the outside of the molecule, and these four B-H bonds consume 8 of our 12 available valence electrons.

We are left with 4 electrons and 2 Hydrogen atoms. These remaining two hydrogens position themselves between the two Boron atoms, acting as a bridge. Each bridging Hydrogen atom shares its 1 electron with the 1 remaining electron from the two Boron atoms. This creates a remarkable bond where three atoms (B-H-B) share only two electrons. This is the famous 3-center-2-electron ($3c-2e$) bond, affectionately known as a banana bond due to its curved electron density.

Now, let's tackle the core question: What is the hybridization of the Boron atom in this intricate setup?

To find the hybridization of any atom, we look at its steric number—the total number of electron domains (bonds and lone pairs) surrounding it. Let's focus on just one of the Boron atoms in our diborane structure.

This single Boron atom is bonded to: 1. Two terminal Hydrogen atoms (via normal $2c-2e$ bonds). 2. Two bridging Hydrogen atoms (via the $3c-2e$ banana bonds).

There are no lone pairs on the Boron atom. Therefore, the total number of bonds (or electron domains) around one Boron atom is exactly 4.

Whenever an atom has a steric number of 4, it must mix four atomic orbitals to accommodate these bonds. It takes one $s$ orbital and three $p$ orbitals, blending them together to form four equivalent $s{p}^3$ hybrid orbitals.

Because the Boron atoms are $s{p}^3$ hybridized, the geometry around each Boron is roughly tetrahedral. This has a profound impact on the overall shape of the molecule.

Diborane is strictly non-planar. The two Boron atoms and the four terminal Hydrogen atoms all lie perfectly flat in a single plane. However, the two bridging Hydrogen atoms sit perpendicular to this plane—one arching above it and the other dipping below it.

Understanding the $s{p}^3$ hybridization is the master key to unlocking the entire 3D architecture of this incredible, electron-deficient molecule.