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Provide the Electronic configuration of \[M{{n}^{2+}}\] and \[C{{r}^{3+}}\]

Answer
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Hint: The distribution of electrons in an element's atomic orbitals is described by its electron configuration. Atomic electron configurations follow a standard nomenclature in which all electron-containing atomic subshells are arranged in a sequence (with the number of electrons they possess indicated in superscript).

Complete answer:
The main quantum number determines the maximum number of electrons that may be accommodated in a shell (n). The shell number is expressed by the formula \[2{{n}^{2}}\], where n is the number of shells. The following are the shells, n values, and total number of electrons that can be accommodated:
SHELLNO OF ELECTRONS
K2
L8
M18
N32

The azimuthal quantum number (abbreviated as ‘l') determines the subshells into which electrons are dispersed.
The value of the primary quantum number, n, determines the value of this quantum number. As a result, when n = 4, four distinct subshells are conceivable.
When n=4 is used. The s, p, d, and f subshells are called after the l=0, l=1, l=2, and l=3 subshells, respectively.
The formula 2(2l + 1) gives the maximum number of electrons that may be handled by a subshell.
As a result, the s, p, d, and f subshells may each hold a maximum of 2, 6, 10, or 14 electrons.
So for Magnesium
It is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{2}}3{{d}^{5}}$
Upon losing 2 electrons from the outermost shell (4s) we get \[M{{n}^{2+}}\]
So the Electronic configuration of \[M{{n}^{2+}}\] is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}3{{d}^{5}}$
So for Chromium
It is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}4{{s}^{2}}3{{d}^{4}}$
Upon losing 3 electrons from the outermost shell 2 from (4s) and one from (3d) we get \[C{{r}^{3+}}\]
So the Electronic configuration of \[C{{r}^{3+}}\] is $1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}3{{s}^{2}}3{{p}^{6}}3{{d}^{3}}$

Note:
The term "Aufbeen" comes from the German word "aufbauen," which means "to build up." According to the Aufbau principle, electrons will first occupy lower-energy orbitals before moving on to higher-energy orbitals.
The sum of the main and azimuthal quantum numbers is used to determine the energy of an orbital. Electrons are filled in the following order according to this principle: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p...