What is the shape name of of an orbital that contain the following electron 3:2:1:1/2 ?
The orbital name is given by the second number (angular quantum number) from the 4 quantum numbers set. l =0 means orbital s, l=1 means orbital p, l=2 means orbital d and l=3 means orbital f.
The quantification rule is `L =l*h/(2*pi)` , in our case `L=2*h/(2pi)`
Now, third number (ml) gives the projection of angular quantum number on a specified axis (usually z axis).
the quantification rule is `L_z =m_l*h/(2*pi)` , in our case
`L_z = -2*h/(2*pi), -h/(2*pi) ,0 ,+h/(2*pi) , +2*h/(2*pi)`
In the case of p orbitals (3 sub-orbitals, `p_x` , `p_y` and `p_z` ) they are perpendicular to each other, but here where we have d orbitals (5 sub-orbitals) the situation is a bit tricky since d sub-orbitals extends simultaneously on two different axis.
Because of this, the following denominations have been given to d sub-orbitals
`m_l=-2` for `d_(xy)` suborbital
`m_l = +2` for `d_(x^2-y^2)` suborbital
`m_l =0` for `d_(z^2)` suborbital
`m_l =-1` for `d_(xz)` suborbital
`m_l =+1` for `d_(yz)` suborbital
Since we do not know the positive direction of z axis for ml =+1 the suborbital is either `d_(xz)` or `d_(yz)` .
Therefore the corresponding suborbital for the quantum numbers 3:2:1:1/2 is either `d_(xz)` or `d_(yz)` .