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No, they do not.
Yes they are both alkaline earth metals in the same group on the periodic table
Beryllium, Calcium or any other element within the same family or group (vertical column on the periodic table)
Calcium and barium are placed in the same vertical column (Group 2) of the periodic table because they have similar chemical properties. They both have two electrons in their outermost energy level, making them part of the alkaline earth metals, which have similar reactivity and properties.
Magnesium belongs to group 2 (alkaline earth metals) in the periodic table. Elements in the same group as magnesium include beryllium, calcium, strontium, barium, and radium. They all share similar chemical properties due to having the same number of electrons in their outermost shell.