Question

If elements with principal quantum number $ n > 4 $ not allowed in nature, the number of possible elements would be
(A) 60
(B) 32
(C) 4
(D) 64

Answer 1

Hint : The number of electrons that can feel a shell is given by twice the square of the quantum number of that shell. The total number of possible electronic configurations will give the total number of elements.

Formula used: In this solution we will be using the following formula;
 $ N = 2{n^2} $ where $ N $ is the number of electrons in a particular orbit, and $ n $ is the quantum number of the orbit.

Complete step by step answer
According to the Pauli Exclusion Principle, no two electrons can occupy the same 4 quantum numbers. These four quantum numbers are; the Principal Quantum Number, the Angular Momentum Quantum Number, the Magnetic Quantum Number, and the Spin Quantum Number.
In general, this allows a particular orbit to contain only a certain amount of electrons. These amounts is given by
 $ N = 2{n^2} $ where $ N $ is the number of electrons in a particular orbit, and $ n $ is the quantum number of the orbit.
Hence, for the first orbit, usually called K shell, the number of electrons will be
 $ N = 2{n^2} = 2{(1)^2} = 2 $
Similarly for the second orbit, we have
 $ N = 2{n^2} = 2{(2)^2} = 8 $
For third orbit
 $ N = 2{n^2} = 2{(3)^2} = 18 $
And finally for the fourth orbit
 $ N = 2{n^2} = 2{(4)^2} = 32 $
Now the total number of elements is given by the total number of electrons.
Hence, the total number of element is
 $ 2 + 8 + 18 + 32 = 60 $
Hence, the correct option is A.

Note
For clarity, the total number of elements is equal to the total number of atoms because; in general, in an atom, elements are determined by the number of protons. When an extra proton is added to an element, a new element is obtained. Hence, for a neutral atom, addition of electrons implies an addition of protons. Thus, the number of new electrons means a different element. Hence, an electron's number from 1-60 means 60 different elements.