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JayKo
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as in Y[tex]^{m}_{l}[/tex], what is l and m mean in their spherical coordinate
jtbell said:What do you mean by "in their spherical coordinate"?
The azimuthal quantum number, l, describes the shape of an electron's orbital. It can have values ranging from 0 to n-1, where n is the principal quantum number. The value of l determines the subshell the electron is in (s, p, d, f) and also affects the energy of the orbital.
The magnetic quantum number, m, specifies the orientation of the orbital in space. It can have values ranging from -l to +l, indicating the number of orbital orientations within a subshell. For example, an s subshell (l=0) only has one possible orientation (m=0), while a p subshell (l=1) has three possible orientations (m=-1, 0, 1).
The maximum number of electrons that can occupy an orbital is 2(2l+1). For example, an s orbital (l=0) can hold a maximum of 2 electrons, a p orbital (l=1) can hold a maximum of 6 electrons, and a d orbital (l=2) can hold a maximum of 10 electrons.
The magnetic quantum number, m, does not directly affect the energy of an orbital. However, different orientations of the same orbital (same values of l and n) have slightly different energies due to the orientation of the electron's spin. This is known as spin-orbit coupling.
The quantum numbers, n, l, and m, are related to each other in that they describe different aspects of an electron's location and energy within an atom. The principal quantum number, n, describes the size and energy level of the orbital. The azimuthal quantum number, l, describes the shape of the orbital. And the magnetic quantum number, m, describes the orientation of the orbital in space.