The splitting of the main spectral line into two or more components with a slight variation in wavelength in the magnetic field is called fine structure in spectroscopy. It means that, in the magnetic field, the electron energy splits to give its sub-states. The electron transitions from these substituent energy levels give additional spectral lines. These are known as fine structures of the main spectral line. The hydrogen spectrum exhibiting the fine structured lines is known as the hydrogen fine spectrum. For more information on this topic, kindly visit our blog at; https://jayamchemistrylearners.blogspot.com/2022/04/fine-structure-of-hydrogen-atom.html

1. Introduction to hydrogen fine
structure
The splitting of the main spectral line into two or more components
with a slight variation in wavelength in the magnetic field is called
fine structure in spectroscopy.
Hydrogen is the lightest element
with a single electron in the
periodic table.
The cleavage of the main spectral
line of the hydrogen atom is due
to the influence of spin-orbit
coupling.
The interaction of spin electron
magnetic moment with the
magnetic field of electron’s relative
motion gives the hydrogen fine
structures.
The splitting of spectral emission
lines of the hydrogen are known
as the hydrogen fine structures.
The hydrogen atom absorbing
external energy shows the
excitation of its electron. In a
hydrogen atom, the transition
of electrons between the two
discrete stationary energy
levels results in the emission of
photons of definite
wavelengths. It shows spectral
lines in the hydrogen
spectrum. Unlike ordinary
spectrometers, a high-
resolution spectrometer
epitomizes the main spectral
line splitting into its
constituents with a slight
variation in their wavelengths.
The hydrogen spectrum
exhibiting the fine structured
lines is known as the hydrogen
fine spectrum.
In 1887, Michelson and
Morely depicted precisely the
absorption trends and spectral
emission lines of hydrogen.
They demonstrated the small
shifts in hydrogen energy
levels and the additional
spectral emission lines in the
hydrogen spectrum. More
clearly speaking, they
explained the fine structure of
the hydrogen atom.
Energy
Increase
Lyman-alpha fine structures
1s-orbital
2s-orbital
2p-orbital
ΔE=hϒ

2. Explanation
The transition of an electron from 1S-orbit to 2P-orbit
gives a spectral line doublet in the presence of the
magnetic field.
The Lyman alpha doublet consists of closely spaced
two spectral emission lines at wavelengths of about
121.5668 nm and 121.5674 nm.
And they are symbolized as Ly-α3/2 and Ly-α1/2
having j values 3/2 and 1/2, where j is the total
angular momentum of the electron.
The electron motion is
associated with the orbital
quantum number (l) and the
spin quantum number (s).
Hence, the total angular
moment quantum number
(j) can be expressed as
j=l+s
(or)
j=l-s
When the electron is in 1S-
orbit, its spin quantum
number values are +1/2 and
-1/2 depending upon the
direction of the magnetic
moment.
Due to the absence of spin-orbit coupling in 1S-orbit, splitting does not
take place in electron energy levels. So, the 1S-orbit has a single energy
level.
In 2P-orbit, the spin-orbit interaction breaks the main energy
level into its components. So, we observe two sub-energy
levels for the electron in the 2P-orbit. The spin angular
momentum quantum number values for the electron are +1/2
and -1/2. Additionally, the orbital angular momentum quantum
number value for P-subshell is 1. The total angular momentum
quantum number values are 1/2 and 3/2.
The hydrogen electron
transition from 1S-orbit to
2P-orbit gives spectral
lines doublet as it involves
the two 2P-orbit energy
sub-states in the electron
transition. The spectral
line doublet is a pair of
two closely spaced
spectral lines with a slight
variation in their
wavelengths.
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The alkali metal
atoms with 1S-
electron in their
valence shell give
spectral line
doublet in the
presence of the
magnetic field.