The elements in same period have same principle quantum number or energy shell.
The elements in same group shows similar chemical and properties.
Explanation:
Inn group:
The elements in same group i.e present in vertical column shows similar chemical properties.
The elements in same group having same number of valance electrons. while in chemical reaction bonds are break and formed and valance electrons are involved. That's why elements in same group having same number of valance electrons and shows similar chemical properties.
In period:
While as we move from left to right the number of valance electron increase by one in every element. But the electron is added in same shell which means that their physical and chemical properties are different but principal quantum number is same.