Given, n = 5, m_l = + 2

For n = 5, possible value of l = 0, 1, 2, 3, 4

For l = 0, m_l = 0

l = 1, m_l =

1, 0, 1

l = 2, m_l =

2, 1, 0, 1, 2

l = 3, m_l =

3, 2, 1, 0, 1, 2, 3

l = 4, m_l =

4, 3, 2, 1, 0, 1, 2, 3, 4

Possible value of m_l for a given value of l

= 0,

1, 2, 3 ..... l

So, number of orbitals having n = 5 and m_l =

2 are 3.