Answer
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Work Step by Step
The periodic table groups together atoms with similar properties, which have the same number of electrons in their outer shells.
The number of electrons in the outer shell depends on the how the electrons are arranged in the atom. The Pauli exclusion principle demands that electrons have different principal quantum number n, angular orbital quantum number $\ell$, magnetic quantum number $m_{\ell}$, and spin quantum number $m_s$.
As atomic number increases, and electrons are added, the exclusion principle shows how they fill the lowest available energy states.
Quantization of orbital angular momentum determines the number of angular momentum states for each n, that is, $\ell$ ranges from 0 to (n-1).
The magnitude of the orbital angular momentum determines how many magnetic quantum states are possible for each orbital angular momentum number, that is, $m_{\ell}$ ranges from $-\ell$ to $\ell$ in whole number steps (i.e., the z-component of the angular momentum is quantized).
Finally, the existence of electron spin means that 2 electrons (spin up and spin down) can fill a subshell that has a particular value of n, $\ell$, and $m_{\ell}$.
In summary, the Pauli exclusion principle, quantization of orbital angular momentum, the quantized direction of angular momentum, and electron spin are the factors that determine the periodicity of the periodic table.
