Determine the angular/ Radial nodes of n=4, l=2, and ml=-2
Does the m sub l value even matter?
If you are determining the number of nodes, and the p orbitals are degenerate, no. However, if the p orbitals are not degenerate then you will have three orbitals but pointed in three directions (along the three axes). YOu can read all about it here.
https://en.wikibooks.org/wiki/General_Chemistry/Shells_and_Orbitals
To determine the angular and radial nodes of an electron in an atom with quantum numbers n, l, and ml, we need to understand the meaning of these quantum numbers and their relationship to the electron's energy and wavefunction.
The principal quantum number (n) determines the energy level or shell of the electron. It can have positive integer values, starting from 1. In this case, n = 4. The value of n indicates that this electron is in the fourth energy level.
The azimuthal quantum number (l) determines the shape or subshell of the electron's orbital. It can have values ranging from 0 to (n - 1). In this case, l = 2. The value of l indicates that this electron is in the d-subshell.
The magnetic quantum number (ml) determines the specific orbital within the subshell. It can have values ranging from -l to +l, including zero. In this case, ml = -2.
Now, let's determine the number of angular and radial nodes:
1. Angular Node (Nl):
The number of angular nodes (Nl) is equal to the difference between l and |ml|.
Nl = l - |ml|
Nl = 2 - |-2|
Nl = 2 - 2
Nl = 0
Therefore, there are no angular nodes (Nl = 0).
2. Radial Node (Nr):
The number of radial nodes (Nr) is determined by the principal quantum number (n) and the angular quantum number (l).
Nr = n - l - 1
Nr = 4 - 2 - 1
Nr = 1
Therefore, there is one radial node (Nr = 1).
To answer your second question, the value of the magnetic quantum number (ml) does not affect the determination of angular and radial nodes. It only specifies the specific orbital within the subshell, but it does not change the overall structure of the electron's wavefunction or the number of nodes.
In summary, for an electron with quantum numbers n = 4, l = 2, and ml = -2, there are no angular nodes (Nl = 0) and one radial node (Nr = 1).