# The periodic table of the elements with $4n^{2}$ $n=2,3,\dots$ periods

## TL;DR

This paper proposes a modified periodic table with $4n^{2}$ periods, redefining periods by halogens and integrating rare-earth elements without separation, supported by ionization energy comparisons.

## Contribution

It introduces a novel periodic table arrangement with $4n^{2}$ periods, redefining period boundaries and maintaining rare-earth elements within the main table.

## Key findings

- Periods are defined by halogens instead of noble gases.
- Ionization energy graphs support the new period structure.
- Rare-earth elements are kept within the main table without separation.

## Abstract

A modification of the standard periodic table of the elements reveals $4n^{2}$ periods, where $n=2,3,\dots$. The new arrangement places hydrogen with halogens and keeps the rare-earth elements in the table proper (without separating them as they are in the standard table). Effectively, periods in the modified table are defined by the halogens rather than by the noble gases. The graph of ionization energy of the elements is presented for comparison of periods in the standard and the modified tables.