Question

An electron has the following quantum number values: n = 3, l = 1, ml = 0. Which of the following notations represents the most likely location of this electron?

Answer 1

Hint: Quantum numbers are a collection of numbers that describe the location and energy of an electron in an atom. Principal, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.

Complete answer:
All you have to do now is match the three quantum numbers' values to an energy shell, an energy subshell, and an orbital.
This will give you a decent sense of where this electron is in an atom.
You already know that the main quantum number, n, indicates the energy shell in which the electron resides. You have n=3 in this situation, which indicates that the electron is in the third energy shell.
The energy subshell in which the electron is situated is determined by the angular momentum quantum number, l. In other words, the sort of orbital that contains the electron is determined by the angular momentum quantum number.
In this example, l=1 indicates that the electron is situated in the p subshell, i.e. in a p orbital.
The orientation of the orbital in which the electron is situated is determined by the magnetic quantum number, ml. In other words, the magnetic quantum number specifies the electron's particular orbital.
 $ l=1\Rightarrow {{m}_{l}}=\{-1,0,+1\} $
Because the magnetic quantum number can have three different values, one electron in the p subshell can occupy three p orbitals.
As is customary, we take $ {{m}_{l}}=0 $
to symbolise the $ {{p}_{z}} $ orbital This indicates that the incomplete quantum number set $ n=3,l=1,{{m}_{l}}=0 $ may be used to represent an electron in the third energy shell, in the 3p subshell, in the $ 3{{p}_{z}} $ orbital—don't forget that you're lacking the value of the spin quantum number, $ {{m}_{s}} $ . This electron can have spin-up, for which $ {{m}_{s}}=+\dfrac{1}{2} $ , or spin-down, for which $ {{m}_{s}}=+\dfrac{1}{2} $ , depending on the magnitude of the spin quantum number.
Hence the location is $ 3{{p}_{z}} $ .

Note:
Quantum numbers define the values of a quantum system's preserved quantities. Electronic quantum numbers (quantum numbers that describe electrons) can be described as a set of numerical values that offer Schrodinger wave equation solutions for hydrogen atoms.