Question

Which of the following sets of quantum numbers correctly represents Beryllium's fourth electron?
N l m s
A) 1 0 0 $ -\dfrac{1}{2} $
B) 1 1 1 $ +\dfrac{1}{2} $
C) 2 0 0 $ -\dfrac{1}{2} $
D) 2 1 0 $ +\dfrac{1}{2} $

Answer 1

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 Step By Step 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 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.
Subshell labels are used to represent an atom's electron arrangement. The shell number (determined by the main quantum number), the subshell name (determined by the azimuthal quantum number), and the total number of electrons in the subshell are all listed in superscript on these labels. 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.
Electronic configuration of Beryllium is $ \text{1}{{\text{s}}^{\text{2}}}\text{2}{{\text{s}}^{\text{2}}} $
The fourth electron is in $ 2{{s}^{2}} $ orbital.
Hence n = 2
l = 0
m = 0
s = $ -\dfrac{1}{2} $
Hence option C is correct.

Note:
Each electron is described as travelling freely in an orbital in an average field generated by all other orbitals in electronic setups. Configurations are characterised mathematically by Slater determinants or configuration state functions. According to quantum physics, each electron configuration has a level of energy associated with it, and electrons may migrate from one configuration to another by emitting or absorbing a quantum of energy in the form of a photon under specific conditions.