Why do you use alphabet k to designate k shell?

Answer 1

It’s just tradition. There is no real reason except that as knowledge expanded we needed ways to identify, define, and communicate – and so many arbitrary designations were assigned to physical entities. Look at the nomenclature of quarks for example – we call the six “flavours” of quarks “up,” “down,” “charm,” “strange,” “top,” and “bottom;” how silly is that?