Question

if quantum nos n= 4 l=1 tell the sub level designation allowable m values and number of orbitals

Answer 1

If Principal Quantum number (n) is 4 then it represents the 4th shell.

Azimuthal Quantum number (l) represents the sub-shell of a Given shell (i.e. 'n')

We know that for a given value of 'n', the values of l range from 0 to (n - 1)

If Principal quantum number (n) = 4 then the values of l range from 0 to 3

If n = 4 and l = 0, it represents 's' sub-shell

If n = 4 and l = 1, it represents 'p' sub-shell

If n = 4 and l = 2, it represents 'd' sub-shell

If n = 4 and l = 3, it represents 'f' sub-shell

The given question is referring to 'p' sub-shell of 4th shell

We know that for a given sub-shell (l), then Number of values of Magnetic quantum number (m) is 2(l) + 1 and the allowable values are given by m = -l to +l

The number 2(l) + 1 represents the number of orbitals, the respective sub-shell contains and the values given to those orbitals are from -l to +l

For 'p' sub-shell : l = 1

⇒ Number of values of Magnetic quantum number (m) for 'p' sub-shell is 2(1) + 1 = 3

⇒ The Sub-shell 'p' contains 3 orbitals and the allowable 'm' values range from -1 to +1

⇒ The Sub-shell 'p' contains 3 orbitals and the values given to those orbitals are -1 , 0 and 1. {we know that they are p(x) , p(y) and p(z)}

With above explanation we can say that Irrespective of 'n', a 'p' sub-shell always contains 3 orbitals and the values of m for those orbitals are -1 , 0 and +1