Question

What are the all four quantum numbers for the $ 19th $ electron in $ Sc(Z = 21) $ ?

Answer 1

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

Complete answer:
The electronic configuration of Scandium is as follows:
 $ Sc = 1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}4{s^2}3{d^1} $
We can see that the $ 19th $ electron goes into $ 4s $ orbital,
For an $ s $ orbital $ l = 0;m = 0 $
Hence, we can say that,
 $ n = 4 $
 $ l = 0 $
 $ m = 0 $
 $ s = + \dfrac{1}{2} $
Hence the four quantum numbers for the $ 19th $ electron in $ Sc $ are $ 4,0,0, + \dfrac{1}{2} $ .
Principal quantum numbers are denoted by the symbol ‘ $ n $ ’. They designate the principal electron shell of the atom.
The azimuthal quantum number describes the shape of a given orbital. It is denoted by the symbol ‘ $ l $ ’ and its value is equal to the total number of angular nodes in the orbital.
The magnetic quantum number determines the total number of orbitals in a subshell as well as their orientation. The sign ‘ $ m $ ’ is used to represent it.
The electron spin quantum number is independent of the values of $ n $ , $ l $ , and $ m $ . The value of this number gives insight into the direction in which the electron is spinning, and is denoted by the symbol ‘ $ s $ ’ .

Note:
Scandium is an element having an atomic number $ 21 $ and represented with the symbol ‘ $ Sc $ ‘ in the periodic table. The metal is silvery-white in colour and has a moderately soft texture. Scandium is mostly used in scientific research. It does, however, have a lot of potential because it has a density that is almost as low as aluminium but a far greater melting point.