By Renuka Miglani|Updated : June 14th, 2023

Are you looking for some short and reliable notes during your CSIR-NET preparations? Then, you have come to a perfect place!

Candidates preparing for their CSIR NET exam might need to get some short study notes and strategies to apply while preparing for the key exam of their life. At this point, We at Byjus Exam Prep come up with short notes on Rotation Spectrawhich comes under the Physical Chemistry section of the Chemical Science syllabus.

Our experienced subject matter experts have meticulously designed this set of short notes on the Rotation Spectra to give you the most standard set of study materials to be focused upon. In this cut-throat competitive world, students need to prepare themselves with the best study materials to help them learn and for their future. So, here we are offering the best study notes that are reliable and can be used by the students during their preparations for the upcoming CSIR-NET 2023 exam.

Consider a diatomic molecule in which m1 and m2 are the masses of the two atoms, and r is the equilibrium bond length, rotating about an axis passing through its centre of gravity,

The centre of gravity is defined by the quality of the momenta about it, i.e.,

...........................(1)

The moment of inertia I of a molecule (rotating as a rigid rotor, not subject to centrifugal forces that tend to distort the molecular geometry and change the moments of inertia) is defined as:

..................................(2)

Here, ri is the difference of the ith particle of mass mi from the centre of gravity. Since a diatomic molecule has two atoms, so,

Therefore, from Eqs. 1 and 5:

....................................(6)

Hence,

Substituting the above values of r1 and r2 in equation 3.

---------------------(7)

--------------------(8)

Where J is the rotational quantum number. The energy of a rotating molecule is given by 1/2Iw2 . Hence, the quantized rotational energy levels of a rigid diatomic rotor (rotating molecule) are given by

------------------(10)

Using the expression for L from Eq. 9,

............................(11)

The expression of total rotational energy is given by:

................................(12)

F(J) is called the rotational term. Defining the rotational constant B as:

.............................(13)

If we want to consider centrifugal distortion whose effect on the diatomic rotor is to stretch the bond and hence to increase the moment of inertia, and thereby to reduce the rotational constant and hence bring the energy levels closer than in the rigid-rotor approximation, then the energy level expression (14a) becomes

F(J) = B J (J + 1) − DJ J2 (J + 1)2 ….............................................. (14c)

Where DJ is the centrifugal distortion constant given by Dj = 4B3/v2, where is the molecule's vibrational frequency.

Next, a selection rule is needed to determine the radiative transition between the rotational energy levels.

..................................(15)

i.e., only those transitions are allowed in which the rotational quantum number changes by unity. The + sign refers to absorption, and the - sign refers to radiation emission. Microwave spectra are usually observed as absorption spectra so that the operative part of the selection rule is ΔJ = +1. For a transition taking place from J to J + 1, the rotational frequency i is given by:

The rotational spectrum of a rigid diatomic molecule consists of a series of lines at 2B, 4B, 6B, 8B, etc. These lines are equally spaced by 2B called frequency separation.