Question

How would you determine the quantum number, ml, for an element?

Answer 1

Hint: There are four quantum numbers for defining the electron in the atom, i.e., Principle quantum number, Azimuthal quantum number, magnetic quantum number, and spin quantum number. The ml represents the Magnetic quantum number and tells the number of orbitals, and it can be calculated with the Azimuthal quantum number.

Complete answer:
There are four quantum numbers for defining the electron in the atom, i.e., Principle quantum number, Azimuthal quantum number, magnetic quantum number, and spin quantum number. The n represents the Principal quantum number and it tells the main shell in which the electron is present. The l represents the Azimuthal quantum number and represents the number of sub-sells in any main shell. The ml represents a magnetic quantum number and represents the number of orbitals present in the subshell. The s represents a spin quantum number, and it tells the direction of the electron.
The ml represents the Magnetic quantum number and tells the number of orbitals, and it can be calculated with the Azimuthal quantum number. For any value of l, we can calculate the ml as –l to +1.
We know there are four sub-shells, i.e., s, p, d, and f. The values of the subshell are:
$s=0$
$p=1$
$d=2$
$f=3$
So, the ml for each subshell will be:
$s=0,\text{ ml = 0}$
$p=1,\text{ ml = -1, 0, +1}$
$d=2,\text{ ml = -2, -1, 0, +1, +2}$
$f=3,\text{ ml = -3, -2, -1, 0, +1, +2, +3}$
Therefore, there is one orbital in s-subshell, three orbitals in p-subshell, five orbitals in d-subshell, and seven orbitals in f-subshell.
For example the value of ml of 2p will be:
$n=2$
$l\text{ is p, l = 1}$
$ml=-1,\text{ 0, +1}$

Note:
We can calculate the value of l from the value of n (principal quantum number). Suppose the value of n is 2, so the value of l will be 0 and 1, because
$l=0\text{ to n-1}$
The values of spin quantum number are fixed, i.e., either the value will be $+{\displaystyle \frac{1}{2}}$ or $-{\displaystyle \frac{1}{2}}$.