Sodium and aluminium have atomic numbers 11 and 13, respectively. They are separated by one element in the periodic table and have valencies 1 and 3 respectively. Chlorine and potassium are also separated by one element in the periodic table (their atomic numbers being 17 and 19, respectively) and yet both have valency 1. Explain.

Sodium and aluminium both belong to period 3 of the periodic table. They are the first and the third elements of their period belonging to group IA and IIIA, respectively. As they lie towards the left in their period, they exhibit metallic character and being separated by one element exhibit positive valencies of +1 and +3, respectively.
On the other hand, even though chlorine and potassium are also separated by one element, chlorine belongs to period 3 and potassium to period 4 of the periodic table. Chlorine is the rightmost element of period 3 belonging to the Halogens group VIIA. So, it exhibits a negative valency of -1. Potassium is the leftmost element of period 4 belonging to the Alkali metals group IA. So, it exhibits a positive valency of +1.