Question

Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers (n, l, ml, ms), prove that the maximum number of electrons in a subshell is 2n².

Answer 1

The Pauli exclusion principle can be defined as: two electrons cannot have the same or equal set of quantum numbers. The highest number of electrons in a subshell is 2n².

Step-by-step explanation:

The Pauli exclusion principle states that each electron in an atom must have unique values for the quantum numbers n, l, ml, and ms. The quantum number n corresponds to the shell, l corresponds to the subshell, ml corresponds to the orientation of the subshell in space, and ms corresponds to the spin of the electron.

The maximum number of electrons that can be in a subshell is determined by the values of the quantum numbers n and l. The formula to calculate the maximum number of electrons in a subshell is 2(2l+1). Since the maximum value for l is n-1, the maximum number of electrons in a subshell is 2(2(n-1)+1) = 2(2n-2+1) = 2(2n-1) = 2n².

Therefore, the maximum number of electrons in a subshell is 2n².