Question

The maximum number of electrons that can be accommodated in an orbit is

• A. $2n^2$
• B. $2n$
• C. $2n+1$
• D. $n^2$

Answer 1

Answer: (A)

$2n^2$

Answer 2

The question asks for the maximum number of electrons that can be accommodated in an orbit. In the context of atomic structure, "orbit" is often used interchangeably with "shell" or "main energy level," which is designated by the principal quantum number 'n'.

According to the quantum mechanical model of the atom:

1. Each main energy level (shell) 'n' contains a total of $n^2$ orbitals.
2. According to Pauli's Exclusion Principle, each orbital can accommodate a maximum of two electrons with opposite spins.

Therefore, the maximum number of electrons that can be accommodated in a shell (or orbit) with principal quantum number 'n' is: Maximum electrons = (Number of orbitals in the shell) $\times$ (Maximum electrons per orbital) Maximum electrons = $n^2 \times 2$ Maximum electrons = $2n^2$

For example:

• For n=1 (K shell), maximum electrons = $2(1)^2 = 2$
• For n=2 (L shell), maximum electrons = $2(2)^2 = 8$
• For n=3 (M shell), maximum electrons = $2(3)^2 = 18$
• For n=4 (N shell), maximum electrons = $2(4)^2 = 32$

The maximum number of electrons in an orbit (shell) is determined by the principal quantum number 'n'. A shell 'n' contains $n^2$ orbitals. Each orbital can hold a maximum of 2 electrons. Thus, the total maximum electrons in a shell 'n' is $2 \times n^2 = 2n^2$.