Question

Elements up to atomic number $103$ have been synthesized and studied. If a newly discovered element is found to have an atomic number $106$, its electronic configuration will be:
A. $\left[ {Rn} \right]5{f^{14}},{\text{ }}6{d^4},{\text{ }}7{s^2}$
B. $\left[ {Rn} \right]5{f^{14}},{\text{ }}6{d^1},{\text{ }}7{s^2},{\text{ }}7{p^3}$
C. $\left[ {Rn} \right]5{f^{14}},{\text{ }}6{d^6},{\text{ }}7{s^0}$
D. $\left[ {Rn} \right]5{f^{14}},{\text{ }}6{d^5},{\text{ }}7{s^1}$

Answer 1

The question is based on Aufbau's principle. The filling up of electrons in various shells of the periodic table is given by Aufbau.

Complete step by step answer:
The elements in the periodic table are arranged in increasing order of the number of protons. This is also equal to the number of electrons.
The Aufbau’s principle states that in the ground state of an atom the electrons in various orbitals are filled up in increasing order of energies of the orbitals. That means the lower energy orbital is filled up first and then the higher energy orbital.
The energy of various orbitals in increasing order is expressed according to the following diagram.
Thus the orbitals are filled up in the order of increasing energies as $1s,{\text{ }}2s,{\text{ }}2p,{\text{ }}3s.{\text{ }}3p,{\text{ }}4s,{\text{ }}3d,{\text{ }}4p,{\text{ }}5s,{\text{ }}4d,{\text{ }}5p,{\text{ }}6s,{\text{ }}4f,{\text{ }}5d,{\text{ }}6p,{\text{ }}7s,{\text{ }}5f,{\text{ }}6d,{\text{ }}7p,{\text{ }}8s$ and so on.
The given set of electronic configuration has the noble gas Radon ($Rn$) with atomic number $86$. The electronic configuration of $Rn$ is $\left[ {Xe} \right]4{f^{14}}5{d^{10}}6{s^2}6{p^6}$. As Radon is a noble gas element in the periodic table so all the orbitals are completely filled up.
The newly discovered element has an atomic number of $106$. Thus $106 - 86 = 20$ electrons will be filled in increasing order of energy of the orbitals.
The $20$ electrons are filled in $7s$, $5f$ and $6d$ orbitals. So of the four given options option A is the correct answer, the electronic configuration of the element with atomic number $106$ is $\left[ {Rn} \right]5{f^{14}},{\text{ }}6{d^4},{\text{ }}7{s^2}$.
And hence option A is the correct answer.

Note:
The electrons in an atomic orbital are filled up in increasing order of energy of the orbitals. The pairing of the electrons in an orbital will not occur until all the orbitals are singly filled according to Hund’s rule of maximum spin multiplicity.