Question

What is the number of the lowest energy level that has a p sublevel?

Answer 1

`n = 2`.

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If we seek the lowest energy level (given by the principal quantum number `n`) for which the `p` orbital sublevel exists, we look for the minimum `n` for which `l`, the angular momentum quantum number, is valid.

The principal quantum number is defined as:

`n = 1, 2, . . .`, in integer steps

and the angular momentum quantum number is defined as:

`l = 0, 1, 2, . . . , n-1`, in integer steps, where `l_max = n - 1`.

Since `p` orbitals have `l = 1`, we must have that if `l_max = n-1 = 1` is the maximum possible `l` we can achieve for a given `n`, then `bb(n = 2)` is the minimum required quantum level for `p` orbitals to exist.

Likewise...

• `n = 1` is the minimum `n` for which `s` orbitals exist.
  (`l_max = n - 1 = 0`.)
• `n = 3` is the minimum `n` for which `d` orbitals exist.
  (`l_max = n - 1 = 2`.)
• `n = 4` is the minimum `n` for which `f` orbitals exist.
  (`l_max = n - 1 = 3`.)

etc.