How many nodal levels for the Dxy orbital

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Quantum numbers

To solve the Schrödinger equation for the hydrogen atom, it is also necessary to introduce quantum numbers that characterize the type of orbitals:

Principal quantum number: n = 1, 2, 3 ... The principal quantum number characterizes the main energy level, the Bohr shell, and corresponds to Bohr's quantum number n.

Secondary quantum number: l = 0 ... (n-1) The secondary quantum number characterizes the shape (symmetry) of the orbitals. Instead of the secondary quantum number, letters are generally given. This corresponds to

(The terms s, p, d, f come from spectroscopy, the results of which, as is well known, gave the impetus for the development of quantitative models before Bohr.

Magnetic quantum number: m = -l ... 0 ... + lThe magnetic quantum number provides information about the orientation of the orbital in space.

Since the value of n limits the possible values ​​of l and m in turn depends on l, only certain combinations of quantum numbers are possible, each of which corresponds to an orbital:

Orbitals with the same minor and magnetic quantum numbers have the same shape (symmetry) but different sizes with different main quantum numbers (1s, 2s, 3s or 2p, 3p, 4p).

So the s orbital is spherical:

as the principal quantum number increases, the area with high charge density increases rapidly. For n = 1, the maximum of the charge density is exactly at Bohr's radius. The 2s orbital (K shell, n = 2) has a maximum electron density at six times the Bohr radius. In addition, a spherical nodal plane (electron density = 0) occurs between two areas of increased electron density. Finally, the 3s orbital is spatially even wider and has two spherical nodal planes.