Question

Which angles are associated with the following orbitals $sp$, $sp^{2} $ and $sp^{3}$?

Answer 1

Hint: The process of forming new degenerate atomic orbitals is called hybridization. Hybridized Orbitals are formed by the mixing of two atomic orbitals such as one ‘s’ and one ‘p’ which have the same energy level. The atomic orbitals formed by hybridization are $sp$, $sp^{2} $ and $sp^{3}$.

Complete answer:
Hybridization and the bond angle of atomic orbitals are related to each other. The hybridized orbitals have some percent of an s orbital and p orbital depending on the type of hybridization.We know that the percent of ‘s’ character in a hybrid molecule is directly proportional to its bond angle. If the percent of ‘s’ orbital increases the angle between the bonds also increases.
Let's have a look at each hybridization of orbitals and the bond angle they possess.
1.$sp$ hybridized orbitals
sp orbitals are formed when one ‘s’ orbitals overlap with one ‘p’ orbital in a similar main shell of the atom. It results in the formation of two new orbitals, so the ‘s’ character is $50%$ and the ‘p’ character is $50%$.
$sp$ hybridized orbitals form a linear structure in space. Thus, the bond angle between them is $180^{0}$.
2.$sp^{2} $ hybridized orbitals
$sp^{2} $ orbitals are formed when one ‘s’ orbitals overlap with two ‘p’ orbitals in the similar main shell of the atom. It results in the formation of three new orbitals, so the ‘s’ character is $33.33%$ and the ‘p’ character is $66.66%$ as the p orbitals are double than the s orbital.
$sp^{2} $ hybridized orbitals form a triangular planar structure in space. Thus, the bond angle between them is $120^{0}$.
3.$sp^{3}$ hybridized orbitals.
$sp^{3}$ orbitals are formed when one ‘s’ orbitals overlap with three ‘p’ orbitals in a similar main shell of the atom. It results in the formation of four new orbitals, so the ‘s’ character is $25%$ and the ‘p’ character is $75%$ as the p orbitals are triple the s orbital.
$sp^{3}$ hybridized orbitals form a tetrahedral structure in space. Thus, the bond angle between them is $109.28^{0}$
Final answer: Bond angle associated with the orbitals are as follows:

Orbital	Bond Angle
$sp$	$180^{0}$
$sp^{2} $	$120^{0}$
$sp^{3}$	$109.28^{0}$

Note:
To find the bond angles between hybridized orbitals, you can divide the number of orbitals formed by $360^o$. However, in $sp^{3}$ hybridized orbitals the bond angle goes more than $90^o$, as there is repulsion between the orbitals. This also changes the geometry of the atom.