### Video Transcript

If π equals one, how many possible
values of π are there?

Firstly, π is the principal
quantum number. π determines the size of an atomic
orbital. π can only be a positive integer
from one to seven. If we compare the spherical 1s and
2s orbitals, the 2s orbital is larger. Itβs important to remember that π
also tells us the energy level in which an electron is found.

Now, the quantum number π has a
few names: the subsidiary, azimuthal, or orbital angular momentum quantum
number. In this video, we will refer to π
as the subsidiary quantum number. This quantum number describes the
shape of an atomic orbital. π can have integer values from
zero to π minus one. The following table shows the type
of orbital associated with each π-value. s orbitals are spherical, while p orbitals
are dumbbell shaped. The shapes of d and f orbitals are
far more complex and difficult to draw.

Now, letβs practice determining the
possible values for π when given a value for π. Letβs do this for only the first
three energy levels.

If π is three, π has values from
zero to π minus one, which means the possible values of π are zero, one, and
two. We can see that each π-value
corresponds to the type of subshells that the third energy level contains. If π is two, there are only two
possible values for π, which correspond to the 2s and 2p subshells inside energy
level two. Finally, if π is one, the only
possible value of π is zero, and the first energy level contains only the 1s
subshell.

In conclusion, if π equals one,
there is only one possible value for π.