Question

How to describe the electrons defined by the following quantum numbers?
 $ n=3,\text{ }l=0,\text{ }{{m}_{l}}=0 $ and $ n=2,\text{ }l=1,\text{ }{{m}_{l}}=1 $ .

Answer 1

Hint :We must know that stands for principal quantum number and stands for azimuthal quantum number. The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital.

Complete Step By Step Answer:
Let’s start with discussing quantum numbers; Quantum numbers are the set of numbers which help us determine the position and energy levels of electrons in an atom. There are four quantum numbers which are principle, azimuthal, magnetic and spin quantum numbers. The Principal quantum number is denoted by and it ranges from one to infinity.
the principal quantum number, $ n $ ; the energy shell in which the electron is located because you know the value of $ n $ .
the angular momentum quantum number, $ l $ ; the energy subshell in which you can find the electron because you know the value of $ l $ .
the magnetic quantum number, $ {{m}_{l}} $ ; the orientation of the orbital in which the electron resides because you know the value of $ {{m}_{l}} $ .
The first set we have is; $ n=3,\text{ }l=0,\text{ }{{m}_{l}}=0 $
This set describes an electron is located in the third energy shell because $ n=3 $
This set describes an electron is located in the s subshell because $ l=0 $
This set describes an electron is located in the s orbital because $ {{m}_{l}}=0 $
Similarly, the second set we have is; $ n=2,\text{ }l=1,\text{ }{{m}_{l}}=1 $
This set describes an electron is located in the third energy shell because $ n=2 $
This set describes an electron is located in the s subshell because $ l=1 $
This set describes an electron is located in the s orbital because $ {{m}_{l}}=1 $
So for this electron, you have the second energy shell, the $ 2p $ subshell, and one of the three $ 2p $ orbitals, let's say $ 2{{p}_{x}}. $ Once again, you don't have the value of $ {{m}_{s}} $ , so we can't say anything about the spin of the electron.

Note :
Note that determining the number of electrons in each shell or subshell is of almost importance as it helps us identify the position of the electrons in the atom. This also helps us understand how many shells and subshells there are in a particular principle quantum.