Question

What electrons could have quantum numbers.
$n = 2,l = 1,{m_l} = 0,{m_s} = + \dfrac{1}{2}?$

Answer 1

The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers. The values of the conserved quantities of a quantum system are given by quantum numbers.

Complete answer:
The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. Quantum numbers are important because they can be used to determine the electron configuration of an atom and the probable location of the atom's electrons.
The angular momentum quantum number,$1$, essentially tells you the subshell in which the electron resides. The values of the $1$ quantum number correspond to:
$\begin{gathered} l = 0 \to s - subshell \\\ l = 1 \to p - subshell \\\ l = 2 \to d - subshell \\\ l = 3 \to f - subshell \\\ \end{gathered}$
We know that the principal quantum number,$n = 2$, is used to describe an electron located on the second energy level.
We have,$ml = 0$, which means that your electron is located in the $2pz$ orbital.
Finally, the spin quantum number,$ms$, which tells us the spin of the electron.
We have two possible values, $- \dfrac{1}{2}$ for spin-down and $+ \dfrac{1}{2}$ for spin-up.
We have, the value $1 = 1$ means that your electron is located in the $p -$subshell, more specifically, in the $2p -$subshell.
The magnetic quantum number,$ml$, tells you the exact orbital in which the electron is located.
The $p -$subshell contains a total of three orbitals, by convention corresponds as
$ml = 0 \to 2pzorbital \\\ ml = 1 \to 2pyorbital \\\ ml = + 1 \to 2pxorbital \\\ \\\$
We have that the quantum number set given to you describes an electron
-located on the second energy level $\to n = 2$
-located in the 2p-subshell $\to l = 1$
-located in the 2pz orbital $\to ml = + \dfrac{1}{2}$

Note:
The combination of all quantum numbers of all electrons in an atom is described by a wave function that complies with the Schrodinger equation. Quantum numbers are also used to understand other characteristics of atoms, such as ionization energy and the atomic radius.