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Chemist20
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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 I am thinking that the fact that there are angular nodes in 2p and not in 2s MUST affect the energy!
Bill_K said:It's an "accidental" degeneracy of course, but qualitatively here's why: the energy depends only on the principal quantum number n = ℓ + nr + 1 where nr 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.
Bill_K said:It's an "accidental" degeneracy of course, but qualitatively here's why: the energy depends only on the principal quantum number n = ℓ + nr + 1 where nr is the radial quantum number
Chemist20 said:why does it only take it into account when we talk about multi electron atoms??
Chemist20 said:I don't get why for hydrogenic atoms the 2s and 2p orbitals have the same energy. i do get it mathematically, but I am thinking that the fact that there are angular nodes in 2p and not in 2s MUST affect the energy!
phyzguy said:Your intuition is correct. In reality they don't have the same energy. The relativistic corrections and the spin-orbit coupling breaks the degeneracy.
The Bohr model is a simplified representation of the structure of an atom, proposed by Niels Bohr in 1913. It states that electrons orbit the nucleus in specific energy levels, with each level corresponding to a specific amount of energy. In hydrogenic atoms, the energy levels are determined by the attraction between the positively charged nucleus and the negatively charged electron.
The energy levels in hydrogenic atoms are calculated using the Rydberg formula, which states that the energy of an electron in a specific energy level is proportional to the inverse of the square of the principal quantum number (n). This formula can be used to calculate the energy levels for any hydrogenic atom, including hydrogen, helium, and lithium.
Energy levels in hydrogenic atoms have discrete values because of the quantization of energy. According to quantum mechanics, energy exists in discrete packets called quanta. This means that the energy of an electron in an atom can only have certain specific values, and cannot have values in between.
Electrons in hydrogenic atoms can transition between energy levels by absorbing or emitting photons of specific energies. When an electron absorbs a photon, it gains energy and moves to a higher energy level. Conversely, when an electron emits a photon, it loses energy and moves to a lower energy level. These transitions are responsible for the emission and absorption spectra of hydrogenic atoms.
The energy levels in hydrogenic atoms play a crucial role in understanding the behavior and properties of these atoms. They determine the electronic structure of the atom, which in turn affects its chemical and physical properties. The energy levels also help explain the spectral lines observed in hydrogenic atoms, providing valuable information about their composition and behavior.