Increasing order of the size of various hybrid orbitals is

\(sp^3 > sp^2 > sp\)

The correct answer is option 2. \(sp^3 > sp^2 > sp\).

Let us delve into why the order \(sp^3 > sp^2 > sp\) is correct in terms of the size of the hybrid orbitals.

Understanding Hybrid Orbitals

Hybridization involves the mixing of atomic orbitals to form new hybrid orbitals. The character of these hybrid orbitals is determined by the proportion of s and p orbitals involved. The extent of the s and p character affects the size of the hybrid orbitals.

Hybrid Orbitals and Their Composition

\(sp\) Hybrid Orbitals:

Composition: 50% s-character, 50% p-character. Since the s orbital is more compact and closer to the nucleus than the p orbital, having a significant amount of s-character makes the \(sp\) hybrid orbitals smaller and more contracted.

\(sp^2\) Hybrid Orbitals:

Composition: 33.33% s-character, 66.67% p-character. These orbitals have less s-character and more p-character compared to \(sp\) orbitals, making them slightly larger and more diffuse.

\(sp^3\) Hybrid Orbitals:

Composition: 25% s-character, 75% p-character. With the least s-character and the most p-character, \(sp^3\) hybrid orbitals are the most diffuse and largest in size.

Influence of s and p Character

s-Character: The greater the s-character, the closer the orbital is to the nucleus and the more compact it is. s orbitals are spherical and located close to the nucleus.

p-Character: The greater the p-character, the more extended the orbital is. p orbitals have a dumbbell shape and extend further from the nucleus compared to s orbitals.

Sizes of Hybrid Orbitals

\(sp\) Orbitals: With 50% s-character, these are the most compact because they have a high proportion of the tightly bound, smaller s orbital influence.

\(sp^2\) Orbitals: With 33.33% s-character and 66.67% p-character, these orbitals are larger than \(sp\) orbitals due to the increased influence of the larger p orbitals.

\(sp^3\) Orbitals: With 25% s-character and 75% p-character, these are the largest hybrid orbitals, dominated by the p orbital's more extensive nature.

Given the above details, the order of increasing size of the hybrid orbitals (from most compact to most diffuse) is

\(sp\) (most compact, highest s-character)

\(sp^2\) (intermediate size, moderate s-character)

\(sp^3\) (most diffuse, lowest s-character)

This correctly aligns with the option \(sp^3 > sp^2 > sp\). Therefore, the correct order of the sizes of various hybrid orbitals is: \(sp^3 > sp^2 > sp\)