The reason the Periodic Table looks this way is because of where the last electrons are being placed into the electron cloud. The Periodic Table is arranged by atomic number (# protons), but for neutral atoms, with each new proton comes another electron. So we can also say that as a result of the atomic number, for a neutral atom, the Periodic Table is also arranged by increasing number of electrons.
With each period, electrons are being placed in a higher energy level (Principle Quantum Number). Their location can also tell us which shape (Orbital Quantum Number) the last electron is placed. See the picture below.

Using the Periodic Table it is possible to determine the electron configuration of an element.
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