Question

If each orbital can hold a maximum of 3 electrons, the number of elements in the 4th [period of the] periodic table (long form) is?

Answer 1

An atomic orbital is a mathematical function in atomic theory and quantum physics that describes the position and wave-like behaviour of an electron in an atom. This function may be used to determine the likelihood of locating any atom's electron in any given area surrounding the nucleus. The phrase atomic orbital can also refer to the actual region or space in which the electron can be calculated to be present, based on the orbital's mathematical structure.

Complete answer:
The atomic orbital model, a contemporary framework for viewing the submicroscopic activity of electrons in matter, is built around atomic orbitals. In this concept, a multi-electron atom's electron cloud is made up of electron configurations that are the result of simpler hydrogen-like atomic orbitals.
Although for higher values of the quantum number n, particularly when the atom in question bears a positive charge, the energies of certain sub-shells become very sizable, the repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons that occupy a complete set of s, p, d, and f atomic orbitals, respectively.
On the premise that each orbital may carry a maximum of two electrons, the n=4 permissible orbitals for the fourth period are s,p,d, and f.
Two electrons are held in the s orbital.
6 electrons are held in the p orbital.
The d orbital has ten electrons.
The f orbital has 14 electrons in it.
The total number of electrons retained in the n=4 shell is 32.
If each orbital can hold three electrons.
If each orbital can hold three electrons.
This shell's total number of electrons $=\dfrac{32}{2}\times 3=48$ electrons
This is the maximum number of components that can be used in the fourth period.

Note:
Atomic orbitals can be uniquely described by a set of integers known as quantum numbers due to the quantum mechanical structure of electrons orbiting a nucleus. These quantum numbers only appear in specific value combinations, and their physical meaning varies depending on whether real or complex versions of the atomic orbitals are used.