Why does total angular momentum cause energy splitting in Lyman Hydrogen series?

In summary, the Lyman series of the Hydrogen atom occurs on the n = 2 level due to electron orbital coupling. This coupling results in 3/2 and 1/2 total angular momentum for the n = 2 level. However, the energy level in the quantum mechanical derivation of the Hydrogen atom's orbitals is only dependent on the n quantum number, and the p orbitals are degenerate due to the possible set of m numbers. The energy splitting caused by total angular momentum is due to the relativistic correction of spin-orbit coupling in the non-relativistic Hamiltonian, which only has the Coulomb interaction potential.
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I have read that Lyman series of Hydrogen atom occur on the n = 2 level, and it is due to electron orbital coupling.

Suppose I understand what is an electron-orbital coupling, and that one gets 3/2 and 1/2 total angular momentum for n = 2 level.

But, from quantum mechanical derivation of the orbitals of Hydrogen atom, the energy level depends only on n quantum number, and that p orbitals caused by possible set of m numbers are degenerate.

How total angular momentum causes energy splitting, if electron-orbital coupling is due to spin and angular momenta which are degenerate?

Thank you.
 
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Relativity. The degeneracy is present in the non-relativistic Hamiltonian, where the only potential term is the Coulomb interaction. Spin-orbit coupling comes from a relativistic correction.
 
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FAQ: Why does total angular momentum cause energy splitting in Lyman Hydrogen series?

What is Lyman Hydrogen splitting?

Lymann Hydrogen splitting is a process in which a hydrogen atom's electron is excited to a higher energy level, and then falls back to its original energy level, emitting a photon in the process.

How is Lyman Hydrogen splitting related to the Lyman series?

The Lyman series is a series of spectral lines in the ultraviolet region that are produced when the electron in a hydrogen atom falls back to its ground state after being excited to higher energy levels. Lyman Hydrogen splitting is the process that produces these spectral lines.

What is the significance of Lyman Hydrogen splitting in astrophysics?

Lyman Hydrogen splitting plays a crucial role in understanding the properties of objects in space, such as stars and galaxies. By studying the wavelengths of the Lyman series lines, scientists can determine the temperature and composition of these objects.

Can Lyman Hydrogen splitting occur in other atoms besides hydrogen?

Yes, Lyman Hydrogen splitting can also occur in other atoms with similar energy level structures, such as helium and lithium. However, the spectral lines produced would be in different regions of the electromagnetic spectrum.

How is Lyman Hydrogen splitting used in laboratory experiments?

In laboratory experiments, Lyman Hydrogen splitting is used to study the properties of hydrogen atoms and their behavior under different conditions. This can provide valuable information for research in fields such as atomic physics and quantum mechanics.

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