Question

Elements of group 1 and group 17 have both valency 1. Why?

Answer 1

because group 1 has only one valence electrons it can loose only 1 electron but in group 17 has 7 valence electrons it gain only 1 election. so group 1 and 17 has only 1 valency.

Answer 2

Elements of group 1 (Lithium, Sodium, Potassium, Caesium, and Francium) have only one electron on their outermost shell. So to gain stability (octet or duplet in the outermost shell) they donate one electron to gain a positive valency of magnitude 1 (+1).  

Group 17 elements (‘Fluorine’, ‘Chlorine’, ‘Bromine’, ‘Iodine’, and ‘Astatine’) have seven valence electrons. So to gain stability of octet in their valence shell, they accept an electron gaining a unit negative charge (-1).