Question

Pauli’s Exclusion principle states that:
A.The nucleus of an atom is negatively charged
B.Electrons enter into the lowest-energy orbitals.
C.Electrons revolve around the nucleus in circular orbitals
D.No two electrons in an atom can have all the four quantum numbers identical.

Answer 1

Hint: The knowledge of the principles of atomic structure is required to solve this question. Pauli’s exclusion principle is regarding the values of the quantum numbers that an electron in an orbital can have.

Complete Stepwise Solution:
There are four different quantum numbers for each electron. Firstly, the principal quantum number (n) which designates the main orbit or the shell or the electron, secondly the azimuthal quantum number (l) which designates the subshell in which the electron is present, thirdly the magnetic quantum number (m) which designates the orbital number in which the electron is present, and lastly the spin quantum number (s) which designates the direction of spin of the electron.
According to Pauli's exclusion principle, “No two electrons will have the same set of all four quantum numbers”.

Hence, statement D is the correct answer.

Notes:
To explain the Pauli’s exclusion principle, let us consider the following example. The atomic number of hydrogen is 1, so its electronic configuration is \[1{{\text{s}}^{2}}\]. So the electrons occupy the first orbit with principal quantum number 1. The azimuthal quantum number for the s-subshell is 0. The magnetic quantum number for the s-subshell is always 0. Now the spins of the electrons present in the same orbital will always oppose each other. Hence the value of spin for one of them will be $\left( +\dfrac{1}{2} \right)$ while the other one will be $\left( -\dfrac{1}{2} \right)$. So the two sets of quantum numbers will be (1, 0, 0, $\dfrac{1}{2}$) and the other set will be (1, 0, 0, $-\dfrac{1}{2}$).