Video Transcript
If 𝑛 equals one, how many possible
values of 𝑙 are there?
Firstly, 𝑛 is the principal
quantum number. 𝑛 determines the size of an atomic
orbital. 𝑛 can only be a positive integer
from one to seven. If we compare the spherical 1s and
2s orbitals, the 2s orbital is larger. It’s important to remember that 𝑛
also tells us the energy level in which an electron is found.
Now, the quantum number 𝑙 has a
few names: the subsidiary, azimuthal, or orbital angular momentum quantum
number. In this video, we will refer to 𝑙
as the subsidiary quantum number. This quantum number describes the
shape of an atomic orbital. 𝑙 can have integer values from
zero to 𝑛 minus one. The following table shows the type
of orbital associated with each 𝑙-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, let’s practice determining the
possible values for 𝑙 when given a value for 𝑛. Let’s do this for only the first
three energy levels.
If 𝑛 is three, 𝑙 has values from
zero to 𝑛 minus one, which means the possible values of 𝑙 are zero, one, and
two. We can see that each 𝑙-value
corresponds to the type of subshells that the third energy level contains. If 𝑛 is two, there are only two
possible values for 𝑙, which correspond to the 2s and 2p subshells inside energy
level two. Finally, if 𝑛 is one, the only
possible value of 𝑙 is zero, and the first energy level contains only the 1s
subshell.
In conclusion, if 𝑛 equals one,
there is only one possible value for 𝑙.
