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I don't get why for hydrogenic atoms the 2s and 2p orbitals have the same energy. i do get it mathematically, but im thinking that the fact that there are angular nodes in 2p and not in 2s MUST affect the energy!!!!
It's an "accidental" degeneracy of course, but qualitatively here's why: the energy depends only on the principal quantum number n = ℓ + n_{r} + 1 where n_{r} is the radial quantum number, i.e. the number of radial nodes. And so more nodes in the angular direction tends to increase the energy, but it is accompanied by fewer nodes in the radial direction which tends to decrease it.
This holds only for the Coulomb potential, V ≈ -1/r, IIRC.It's an "accidental" degeneracy of course, but qualitatively here's why: the energy depends only on the principal quantum number n = ℓ + n_{r} + 1 where n_{r} is the radial quantum number
In a multi-electron atom, an individual electron "feels" not only the attraction of the nucleus,but also the repulsion of the other electrons. The "effective" potential is not -1/r as with a one-electron atom.why does it only take it into account when we talk about multi electron atoms??
Your intuition is correct. In reality they don't have the same energy. The relativistic corrections and the spin-orbit coupling breaks the degeneracy.I don't get why for hydrogenic atoms the 2s and 2p orbitals have the same energy. i do get it mathematically, but im thinking that the fact that there are angular nodes in 2p and not in 2s MUST affect the energy!!!!
Right... so then why in the H atom the 2s has the same energy as the 2p ?Your intuition is correct. In reality they don't have the same energy. The relativistic corrections and the spin-orbit coupling breaks the degeneracy.