Question

How many electrons can occupy the f-orbitals at each energy level?

Answer 1

Hint: We know that Orbitals are basically energy levels, the number of electrons occupying different energy levels. Orbitals are termed as mechanical functions which tell us the location of electrons in atoms. The probability of finding an electron around the nuclei can be predicted by using this mathematical function.

Complete step by step solution:
We know that s, p, d, f are the subshells in the atoms and the electrons are filled in accordance with the Pauli exclusion principle given by Austrian physicist Wolfgang Pauli in $ 1925. $ Before heading directly to the answer you must first understand the Pauli Exclusion Principle. The Pauli Exclusion Principle states that no two fermions (for example electrons) cannot have all the quantum numbers same and thus cannot occupy the identical quantum state. Thus, each sub-orbital can only hold two electrons with the different spin quantum number.
The orbitals are the space around the nucleus where there is a higher probability to find an electron s,p,d,f are the different subshells which are the collection of few orbitals. s subshell has only one orbital, p subshell has three orbitals, d subshell has five orbitals and f subshell has seven orbitals. Now, according to Pauli exclusion principle, each orbital must have only two electrons, thus, s subshell has two electrons, p subshell has six electrons, d subshell has ten electrons and f subshell has fourteen electrons in total.
The f subshell has a total of seven orbitals, and each orbital can hold two electrons, and so the f subshell can hold a total of $ 7\times 2=14~ $ electrons.

Note:
Remember that we don’t have to remember shapes of all the orbitals, we just have to remember there are seven orbitals in each level from fourth level, similarly orbitals from second level orbitals and it has three orbitals. It is spherically symmetrical in shape, having a nucleus in the center. The energy level gets on increasing as we go away from the nucleus resulting in a bigger size of orbitals.