The maximum number of 90° angles between bond pair-bond pair of electrons is observed in
(a) dsp3 hy

Q: Why doesn't $sp^3$ have any $90^\circ$ angles?

In $sp^3$ hybridization, the geometry is tetrahedral. To minimize repulsion equally in 3D space, the four bonds spread out to an angle of $109.5^\circ$, not $90^\circ$.

Q: What is the geometry of $dsp^2$?

The $dsp^2$ hybridization corresponds to a square planar geometry. Imagine a flat square with the central atom in the middle; the angle between adjacent bonds is $90^\circ$.

Q: Are the equatorial bonds in TBP at $90^\circ$ to each other?

No, the three equatorial bonds in a Trigonal Bipyramidal ($sp^3d$) geometry lie in a single plane and are separated by $120^\circ$ to minimize repulsion.

Q: How do we know which bonds are axial and which are equatorial?

Equatorial bonds lie in the central horizontal plane (like the equator of the Earth). Axial bonds lie along the vertical axis (like the North and South poles), perfectly perpendicular to the equatorial plane.

Q: Why is it called octahedral if it only has 6 bonds?

The term 'octahedral' refers to the shape of the polyhedron formed if you connect all the outer atoms with straight lines. This shape has 8 triangular faces (octa = eight, hedron = face), even though there are only 6 vertices (atoms) attached to the center.

Question

The maximum number of $90^\circ$ angles between bond pair-bond pair of electrons is observed in

Options:

(A) $dsp^3$ hybridisation

(B) $sp^3d$ hybridisation

(C) $dsp^2$ hybridisation

(D) $sp^3d^2$ hybridisation

Sigma Percentile · Accepted Answer

Imagine you are holding a central atom and attaching other atoms to it. The way these atoms arrange themselves in 3D space to minimize repulsion determines the bond angles. This is the core principle of VSEPR theory. Let's visualize the geometries for the given hybridizations to find out which one packs the maximum number of $90^\circ$ angles.

### Analyzing $sp^3d$ Hybridization

First, let's look at $sp^3d$ hybridization. It forms a **Trigonal Bipyramidal (TBP)** geometry. Here, three atoms form an equatorial triangle, and two atoms are placed axially, directly above and below this plane.

Now, how many $90^\circ$ angles are there? The bonds within the equatorial plane are at $120^\circ$ to each other. However, each of the two axial bonds is perfectly perpendicular to the three equatorial bonds. So, for the top axial bond, there are three $90^\circ$ angles. For the bottom axial bond, there are another three.

Mathematically, $2 	imes 3 = 6$. Thus, a TBP geometry has exactly **six** $90^\circ$ angles.

### Analyzing $dsp^2$ Hybridization

Next, consider $dsp^2$ hybridization. This results in a **Square Planar** geometry. All four bonds lie in the same plane, pointing towards the corners of a square.

The angle between any two adjacent bonds in this square is exactly $90^\circ$. Since there are four sides to the square, there are exactly **four** $90^\circ$ angles in a square planar molecule.

### Analyzing $sp^3d^2$ Hybridization

Now, let's shift our focus to $sp^3d^2$ hybridization. This results in a beautiful **Octahedral** geometry. Here, four atoms lie in a square equatorial plane, and two are axial (one above, one below).

Let's count the $90^\circ$ angles here. First, look at the square equatorial plane. Just like in the square planar geometry, the angle between any two adjacent equatorial bonds is exactly $90^\circ$. That gives us **four** angles right there.

But wait, there's more! Each of the two axial bonds is perpendicular to all four equatorial bonds. The top axial bond makes four $90^\circ$ angles with the equatorial plane, and the bottom axial bond makes another four. That's $2 	imes 4 = 8$ additional $90^\circ$ angles.

Adding them up, $4 	ext{ (equatorial)} + 8 	ext{ (axial)} = 12$. An octahedral geometry boasts a whopping **twelve** $90^\circ$ angles!

### The Final Verdict

Comparing all the geometries:
- $dsp^2$ has $4$ angles of $90^\circ$.
- $sp^3d$ has $6$ angles of $90^\circ$.
- $sp^3d^2$ has $12$ angles of $90^\circ$.

Therefore, the maximum number of $90^\circ$ angles between bond pairs is observed in **$sp^3d^2$ hybridization**.

Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: The maximum number of $9 0^{\circ}$ angles between bond pair-bond pair of electrons is observed in

Select Answer:

Visualized Solution

\text{Molecular Geometries}

sp^3d \text{ Hybridization}

90^\circ \text{ Angles in TBP}

sp^3d^2 \text{ Hybridization}

90^\circ \text{ Angles in Equatorial Plane}

90^\circ \text{ Angles from Axial Bonds}

\text{Conclusion}

\text{Food for Thought}

The Sigma Insight: Hybridisation and VSEPR Theory

Analyzing $s p^{3} d$ Hybridization

Analyzing $d s p^{2}$ Hybridization

Analyzing $s p^{3} d^{2}$ Hybridization

The Final Verdict

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Animated Solution for Chemistry - Chemical Bonding and Molecular Structure: .math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } The maximum number of 90∘ angles between bond pair-bond pair of electrons is observed in