Question

The maximum number of electrons in a shell with the principal quantum number = 4 are:
A.2
B.10
C.16
D.32

Answer 1

Hint: To answer this question, you should recall the concept of quantum number. Quantum numbers can be used to describe the trajectory and the movement of an electron in an atom. The number of electrons can be calculated from the formula given.

Formula: $\text{total electron}$$ = 2 \times n^2 $
where n is the shell number.

Complete Step by step solution:
The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers. You should know that four quantum numbers can be used to completely describe all the attributes of a given electron belonging to an atom, these are:
Principal quantum number, denoted by $n$;
Orbital angular momentum quantum number (or azimuthal quantum number), denoted by $l$;
Magnetic quantum number, denoted by $m_l$;
The electron spin quantum number, denoted by $m_s$.
 Formula to determine the number of electrons present in any shell is as follows :
 Let the shell number is $n$ , then the number of electrons present in n shell $= 2n^2$.
Hence, as per formula the number of electrons in fourth shell $= 2 \times 2^4 = 32$

Thus, the correct answer to this question is option D.

Note: The electronic configuration of elements is based on majorly 3 rules:
According to the Pauli’s Exclusion Principle in an atom, no two electrons will have an identical set or the same quantum numbers. There salient rules of Pauli Exclusion Principle are that only two electrons can occupy the same orbital and the two electrons that are present in the same orbital should be having opposite spins.
According to Hund’s Rule of Maximum Multiplicity rule for a given electronic configuration of an atom, the electron with maximum multiplicity falls lowest in energy.
According to the Aufbau principle, the electrons will start occupying the orbitals with lower energies before occupying higher energy orbitals.