Module 2 : Atomic Physics & Atomic Structure
Lecture 23 : Electron Spin resonance spectroscopy
 

Let us start with ground state  of hydrogen atom having single electron. Here, L =0, S = ½, and J = ½. Under the magnetic field this level splits into two energy levels, essentially due to the spin projection ms = ½ and ms = - ½ because mL = 0.
The splitting energy due to the magnetic field is as shown in figure 23.1. The value of gJ = 2.
The transition between this level is governed by the magnetic dipole selection rule
. This transition changes the spin projection by .

Figure-23.1

Since,
(23.1)


Here,  because L = 0

It can be seen that the frequency required for the transition to occur is about 2.8 MHz per Gauss of applied field.
This means that for the magnetic field usually employed in the laboratory, the radiation required belongs to the microwave region.
When the magnetic field used is about 3400 Gauss, the corresponding applied frequency required is in the microwave region of the electromagnetic spectrum (~9 to 10 GHz). This corresponds to a wavelength of about 3.4 cm and is known as the X - band frequency.