Hyperfine Structure

We know that when an atom is subjected to the varying magnetic field we notice that, the spectral lines are further subdivided into closely spaced lines, the process of splitting of spectral lines is known as the hyperfine structure. The hyperfine structure is mainly observed during the Zeeman effect, which explains particularly the splitting of energy levels or the spectral lines in the presence of external magnetic fields. The splitting of energy levels in the Zeeman effect is directly proportional to the applied magnetic field. Such splitting is explicitly known as the hyperfine structure.

Hyperfine Splitting

Many fine structure components of the spectral lines, when they are observed under a high resolution spectrometer, it is noticeable that those fine lines are further subdivided into smaller lines separated by considerably small spacing. And this process of splitting of the spectral line is known as hyperfine splitting or the hyperfine structure.

When we examine the Balmer series of spectral lines we know that it consists of four different spectral lines corresponding to violet, blue, green and red wavelengths. When spectral lines of the hydrogen spectrum examined under a high-resolution spectrometer it was found that a single spectral line appears to be resolved into two pairs of closely spaced single lines such that these split lines will be having slightly different wavelengths. This splitting spectral line is known as the hyperfine structure of a hydrogen atom.

When the red spectral line or which is also known as the H$_{\alpha}$ the line is closely examined with high-resolution spectrometers, physicists found that it consists of two closely spaced doublet lines due to spin-orbit coupling. We know that the electrons are revolving around the nucleus in definite orbitals and due to the orbital motion of electrons a magnetic field is generated. When the spin electron magnetic moment interacts with the magnetic field, this interaction is familiarly known as spin-orbit coupling.

In atomic spectroscopy, the energy levels of electrons of an atom are given by the formula:

⇒ n$^{2s+1}$ l$_{j}$  …..(1)

Where,

n - The principal quantum number

s - The spin angular momentum quantum number

l - The orbital angular momentum quantum number

j - The total angular momentum quantum number (i.e., the sum of both spin and orbital angular momentum i.e., j = l ± s)

Depending upon the value of ldifferent orbits or energy levels are designated, for example, for l = 0 we have S-orbit, for l = 1 we have P-orbit, and so on.

Hyperfine Levels

The hyperfine levels of the spectral line describe the splitting of spectral lines due to the electron spin and the relativistic correction to the total energy of the hydrogen atom electron. When electrons transit from lower energy level to higher energy level by absorbing the energy, it will be unstable and hence loses its energy in the form of photons of different wavelengths that further results in a spectrum.

The interaction between the magnetic field generated due to the relative motion of the nucleus and the electron spin angular momentum will result in the splitting of the energy of electrons into two energy levels.

The electron with +½ will have a magnetic spin momentum and experiences a torque due to the presence of a magnetic field and hence it will rotate it, at the same time, the electron with -½ will also have some magnetic spin momentum and experiences a torque due to the presence of magnetic field and hence it will rotate it in opposite direction. As the electron rotates, there will be a change in its internal energy and it is given by:

⇒ U = - μ • B

(Note: since they rotate by a different amount, hence they will also have a different amount of energy)

Suppose that the electron in hydrogen atom transit from 1s level to 2P level, we know that the motion of the electron is associated with the orbital quantum number and the spin quantum number. When the electron is in the 1S state it is in its own orbit and hence a single energy level is obtained, whereas the 2p state due to spin-orbit interaction splits into two levels. Mathematically, we write:

⇒ j = l ± s

Did You Know:

• As the hyperfine structure is very small, the transition frequencies are usually not located in the optical but are in the range of radio- or microwave (also called sub-millimetre) frequencies.

• Hyperfine splitting gives the 21 cm line observed in H I regions in the interstellar medium.

• Carl Sagan and Frank Drake considered the hyperfine levels of hydrogen to be a sufficiently universal phenomenon so as to be used as a base unit of time and length on the Pioneer plaque and later the Voyager Golden Record.