If the value of n = 2

... The quantum number l can have values from

to.

... The total number of orbitals possible at the n = 2 energy level is.

If the value of l = 3

... The quantum number ml can have values from to.

... The total number of orbitals possible at the l = 3 sublevel is

Principle quantum number, n = 2

l = 0, 1

if l = 0, m = 0

l = 1, m = - 1, 0, + 1

Total number of orbitals = 4

Principle quantum number, n = 3

l = 0, 1, 2

if l = 0, m = 0

l = 1, m = - 1, 0, + 1

l = 2, m = - 2, - 1, 0, + 1, + 2

Total number of orbitals = 9

Explanation:

Principle quantum number, n = 2

L can take values from 0 to n-1.

So, l = 0, 1

The values of m = - l to l

So, if l = 0, m = 0

l = 1, m = - 1, 0, + 1

Total number of orbitals = 4 which are s orbital (l = 0) and 3 p orbitals (l = 1)

Principle quantum number, n = 3

L can take values from 0 to n-1.

So, l = 0, 1, 2

The values of m = - l to l

So, if l = 0, m = 0

l = 1, m = - 1, 0, + 1

l = 2, m = - 2, - 1, 0, + 1, + 2

Total number of orbitals = 9 which are s orbital (l = 0) and 3 p orbitals (l = 1) and 5 d orbitals (l = 2)