Question

Pauli’s exclusion principle states that:
(a)- The nucleus of an atom is negatively charged.
(b)- Electrons enter into lowest-energy orbitals.
(c)- Electrons revolve around the nucleus in circular orbits.
(d)- No two electrons in an atom can have all the four quantum numbers the same.

Answer 1

Hint: There are four quantum numbers for an electron in an atom; these are Principal quantum number (n), Azimuthal quantum number (l), Magnetic quantum number (m), and spin quantum number (s). If 2 atoms have the same n, l, and m, its s would have opposite spins.

Complete answer: From the study of the quantum numbers, Wolfgang Pauli, a German physicist in 1925 put forward a principle known after his name as Pauli’s exclusion principle. It states that:
“No two electrons in an atom can have the same set of four quantum numbers.”
  If one electron in an atom has a particular value for the quantum number, then all the other electrons in that atom are excluded from having the same set of values. It is because of this reason that this principle is called the exclusion principle. Thus, it follows from the above discussion that an atom may have the same values for any of the three quantum numbers but the fourth must be different.
Now, any particular orbital is described by three quantum numbers i.e. n, l, and m. For example, 3s-orbital has \[n=3,l=\text{0 and }m=0\].since for each value of m, there are two values of the spin quantum number, i.e., \[+\dfrac{1}{2}\] and \[-\dfrac{1}{2}\] , therefore, 3s-orbital can have two electrons; one with quantum numbers \[n=3,l=\text{0, }m=\text{0 and }s=+\dfrac{1}{2}\], and the other with quantum numbers, \[n=3,l=\text{0, }m=\text{0 and }s=-\frac{1}{2}\].
Hence, the correct answer is an option (d)- No two electrons in an atom can have all the four quantum numbers the same.

So, the correct answer is “Option D”.

Note: Any given orbital can have two and not more than two electrons. This gives another definition of Pauli's exclusion principle which states that 'An orbital can have a maximum of two electrons and these must have opposite spins.'