Number of IR Active Vibrational Modes in Ammonia

Ammonia (NH3) is a molecule consisting of one nitrogen atom bonded to three hydrogen atoms. It is a trigonal pyramidal molecule with a lone pair of electrons on the central nitrogen atom. This lone pair of electrons and the vibrations of the bonds in the molecule give rise to its infrared (IR) active vibrational modes.

Explanation:

1. Molecular Structure:
Ammonia has a trigonal pyramidal structure with a nitrogen atom at the center and three hydrogen atoms forming bonds with the nitrogen. The nitrogen-hydrogen bonds are polar due to the difference in electronegativity between nitrogen and hydrogen.

2. Symmetry:
The symmetry of a molecule determines its vibrational modes. Ammonia belongs to the C3v point group, which has three symmetry operations: the identity operation (E), a C3 rotation, and three vertical mirror planes (σv).

3. Vibrational Modes:
In ammonia, there are three vibrational modes associated with the stretching and bending of the nitrogen-hydrogen bonds and the lone pair of electrons on the nitrogen atom. These modes can be classified as follows:

- Stretching Mode: The nitrogen-hydrogen bonds can stretch, resulting in symmetric (ν1) and asymmetric (ν3) stretching modes. These modes involve the movement of the atoms along the bond axis.

- Bending Mode: The nitrogen atom can undergo a rocking motion, resulting in the ν2 bending mode. This mode involves the movement of the hydrogen atoms towards or away from the nitrogen atom.

- Lone Pair Mode: The lone pair of electrons on the nitrogen atom can undergo an in-plane wagging motion, resulting in the ν4 bending mode. This mode involves the movement of the lone pair electrons.

4. IR Activity:
For a vibrational mode to be IR active, it must cause a change in the dipole moment of the molecule. In ammonia, the symmetric stretching (ν1) and bending (ν4) modes do not cause a change in the dipole moment and are therefore IR inactive. The asymmetric stretching (ν3) and bending (ν2) modes, however, do cause a change in the dipole moment and are IR active.

5. Counting IR Active Vibrational Modes:
Therefore, the number of IR active vibrational modes in ammonia is the sum of the IR active modes, which is 2. Hence, the correct answer is '2'.

In summary, ammonia has a total of four vibrational modes, but only two of them (asymmetric stretching and bending modes) cause a change in the dipole moment and are IR active. Thus, the number of IR active vibrational modes in ammonia is '2'.