I am terribly confused. I have always been hearing that in the hydrogen atom, 2s and 2p orbitals have the same energy. Similarly, the 3s, 3p and 3d orbitals have the same energies. This is also suggested by the hydrogen spectrum, my professor also believes the same, and I am unable to find anything against this on the internet.(adsbygoogle = window.adsbygoogle || []).push({});

But what is the basis for this degeneracy?

Upon solving the radial equations for 2s and 2p orbitals, we get the same eigenvalue for Energy, that depends only on the principal quantum number n. However, the wave functions also have an angular part and upon solving the angular equations for 2s and 2p we get a zero value for the 2s (angular momentum=0) and a finite value for 2p (angular momentum=root(2)*hbar). This angular momentum will contribute an extra value of root(2)*hbar/(2*I) to the energy. This will immediately give 2s and 2p different energy values, so they cannot be degenerate.

Have I gone wrong somewhere?

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# Degeneracy of Hydrogen atomic orbitals with different l-values but same n-value

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