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What are the four quantum numbers?


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The four quatum numbers  are the principle quantum number, n, the angular momentum quantum number, l, the magnetic quantum number $$m _{l}$$ , and the electron spin quantum number, $$ m _{l}$$
The principle quantum number , n, describes the energy and distance from the nucleus, and represents the shell.
For example, the 3d subshell is in the n=3 shell, the 2s subshell is in the n=2 shell, etc.
The angular momentum quantum number , l, describes the shape of the subshell and its orbitals, where l=0,1,2,3... corresponds to s,p,d, and f subshells (containing s,p,d,f orbitals), respectively.
For example, the n=3 shell has subshells of l=0,1,2, which means the n=3 shell contains s, p, and d subshells (each containing their respective orbitals). The n=2 shell has l=0,1, so it contains only s and p subshells. It is worth noting that each shell has up to n1 types of subshells/orbitals.
The magnetic quantum number , $$m_{l}$$, describes the orientation of the orbitals (within the subshells) in space. The possible values for ml of any type of orbital (s,p,d,f...) is given by any integer value from l to l.
So, for a 2p orbital with n=2 and l=1, we can have $$ m_{l} = -1, 0, 1$$ This tells us that the p orbital has 3 possible orientations in space.

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