Video Transcript
How many electrons in total can
have the quantum numbers 𝑛 equals two and 𝑙 equals one?
Quantum numbers are numbers we
assign to electrons to describe where they are, shell, subshell, and so on. 𝑛 is the symbol given to the
principal quantum number. If 𝑛 equals one, we’re looking at
the first electron shell. If it equals two, we’re looking at
the second. In this example, 𝑛 equals two. So, we’re looking at the second
electron shell. 𝑙 is the symbol used for the
subsidiary quantum number, also known as the orbital angular momentum quantum number
or the subshell number. Each value of 𝑙 corresponds with a
type of subshell, like an s-type or a p-type subshell. With 𝑙 equal to one, we’re dealing
with a p-type subshell.
The question is asking us, how many
electrons in total can have these particular quantum numbers? The key here is that if we’re
looking at the same atom or ion, no two electrons can have exactly the same set of
quantum numbers. So, is the answer one, since we
have quantum numbers 𝑛 and 𝑙 fixed at values of two and one, respectively? Well, no, there are two other
quantum numbers that can uniquely define an electron.
There’s another quantum number that
defines the orbital the electron is in, and that’s known as the magnetic quantum
number. The possible values of the magnetic
quantum number are zero, plus or minus one, plus or minus two until we reach plus or
minus 𝑙, which for a value of one would give the values of 𝑚 𝑙 of negative one,
zero, and one. This means we have three orbitals
in total.
The fourth quantum number we need
is the spin quantum number 𝑚 𝑠, which can either be positive a half or negative a
half. This gives us two possible spin
states. We can now calculate the number of
possible sets of quantum numbers and therefore the number of electrons we can
possibly have. There are two possible values for
the spin quantum number, three values for the magnetic quantum numbers, so that’s
two electrons per orbital, giving us six electrons in total. You could have done this question
simply by remembering that a p-type subshell contains a maximum of six
electrons. But this way, we’ve proved it.
