Question

3. For a linear molecule such as HCl the number of allowed mode of vibrations are:
a. 1
b. 2
c. 4
d. 3​

Answer 1

Because rotation along the molecular axis cannot be detected, a non-linear molecule with N atoms has 3N – 6 normal modes of vibration, whereas a linear molecule has 3N – 5 modes.

Answer 2

Answer:

The number of the allowed modes of vibrations for a linear molecule $HCl$  is $1$.

Therefore, option a) $1$ is correct.

Explanation:

Given data,

The linear molecule is $HCl$.

The number of the allowed modes of vibrations =?

As we know,

• All the atoms present in a molecule are constantly in motion.

These motions can be:

• Translational (external), rotational (internal) and vibrational (internal).

Now, we have to find out the number of vibrational modes:

For linear molecules, the number of vibrational modes:

• $3N-5$

For non-linear molecules, the number of vibrational modes:

• $3N-6$

Here, N = the number of atoms

Now, as given, the molecule is $HCl$ ( linear molecule )

And the number of atoms in $HCl$ = $2$

As we discussed above;

• For linear molecules, the number of vibrational modes = $3N-5$.
• The number of the allowed modes of vibrations = $3(2) -5$ = $1$.