which quantum number, or quantum numbers, can be connected with the direction a particular orbital position points in space, regarding wave mechanics?
If you call the quantum numbers n, l, ml and ms, the ones with directional pointing information are ml (orbital momentum component) and ms (electron spin component)
The quantum number that is associated with the direction a particular orbital position points in space is called the magnetic quantum number, often represented by the symbol "m sub l". The value of the magnetic quantum number determines the orientation or direction of the orbital within a given subshell.
To determine the possible values of the magnetic quantum number, you can use the following formula:
m sub l = -l, -l+1, -l+2, ..., 0, ..., l-2, l-1, l.
In this formula, "l" represents the orbital angular momentum quantum number (also known as the azimuthal quantum number), which specifies the shape of the orbital. The value of the magnetic quantum number ranges from -l to +l, including zero, which gives all possible orientations of the orbital within the subshell.
For example, in the p subshell (l = 1), the possible values of the magnetic quantum number are -1, 0, and 1. This means that there are three p orbitals, each with a specific orientation along the x, y, and z axes.
It's worth noting that the magnetic quantum number is one of the quantum numbers used to describe the overall quantum state of an electron in an atom, along with the principal quantum number (n), the angular momentum quantum number (l), and the spin quantum number (m sub s). These quantum numbers provide a complete description of the electron's energy, orbital shape, orientation, and spin state.