The sentence you provided, "The periodic table is a table arranged the elements in order of their atomic numbers," is not grammatically correct. Here's a revised version:
"The periodic table is a table that arranges the elements in order of their atomic numbers."
In this revised version, the relative pronoun "that" is used to introduce the dependent clause "that arranges the elements." Additionally, the verb "arranges" is added to provide clarity and improve the sentence's grammatical structure.