Question

What are ${m_s}$ and ${m_l}$ for $3p$ electron?

Answer 1

Quantum number defines the properties of the atomic orbital’s and the electrons in those orbitals. There are four quantum numbers in total which describe various information about the atomic orbitals and the electrons present in those orbitals. In other words, to completely describe an electron in an atom, quantum numbers are required.

Complete answer:
For $3p$ electrons, the spin quantum number and magnetic quantum number can be calculated as follows:
Step 1: Calculation of principal quantum number for $3p$ electrons:
Principle quantum number defines the main energy level in which the electrons are present. It is denoted by the symbol‘ $n$ ’. So, in this case the principal quantum number $n = 3$ .
Step 2: Calculation of Azimuthal quantum number for the $3p$ electrons:
Azimuthal quantum number defines the angular momentum of the electrons. It is denoted by the symbol‘ $l$ ’. The value of the Azimuthal quantum number ranges from zero to ( $n - 1$ ) where n is the principal quantum number. But, in this case $l = 1$ as this means the $p$ sub- shell is indicated.
Step 3: Calculation of magnetic quantum number for $3p$ electrons:
The magnetic quantum number defines the number of orbitals in the given sub- shell. It is denoted by the symbol ‘ ${m_l}$ ’. The value of the magnetic quantum number ranges from -1, 0, +l where $l$ is the Azimuthal quantum number. In this case $l = 1$ so the value of magnetic quantum number ${m_l}$ = -1, 0, +1. This means that the $p$ sub- shell has three orbitals.
Step 4: Calculation of spin quantum number for the $3p$ electrons:
Spin quantum number defines the spin orientation of the electrons. It is denoted by the symbol ‘ ${m_s}$ ’. In this case the spin quantum number ${m_s} = + 1/2$ and $- 1/2$ .

Note:
Quantum number can be referred as the address of the electrons as the four quantum numbers i.e. $n$ is the principal quantum number defines the main energy shell, $l$ which is the Azimuthal quantum number defines the orientation of the orbital while ${m_l}$ which is the magnetic quantum number defines the orbitals present in the sub- shell and the ${m_s}$ which is spin quantum number defines the direction of the spin.