Question

Show that the radius of the orbit in hydrogen atom varies as n², where n is the principal quantum numbers of the atom.

Answer 1

For each n there are n subshells(l) from 0 to n-1

Now there are 2l + 1 orbitals for each l (-l to +l)

There are total n values of n and for each l there are 2l + 1 orbitals. ( 1 orbital for l = 0 , 3 orbitals for l = 1 , 5 for orbitals for l = 2 and so on)

Now add 1 , 3, 5, 7 till n terms

So use formula for A.P. to get n^2