An electron was found to have
values of 𝑛 equals two and 𝑙 equals one. How many different orbitals could
this electron be in?
𝑛 and 𝑙 are quantum numbers. Quantum numbers are values that can
be used to completely describe an electron in an atom. 𝑛 is used to represent the
principal quantum number. The value of 𝑛 can be any positive
integer. This quantum number indicates which
electron shell or energy level the electron can be found in. It can also be used to indicate the
relative size of an atomic orbital. As the value of 𝑛 increases, the
electron will be at a higher energy and less tightly bound to the nucleus.
In this question, we are told that
an electron has a principal quantum number of two. 𝑙 is used to represent the
subsidiary quantum number. This quantum number indicates the
type of subshell or orbital shape in which the electron is found. The possible values for the
subsidiary quantum number depend on the principal quantum number. 𝑙 can be any positive integer from
zero to 𝑛 minus one, with each value representing a different subshell. So when 𝑛 equals two, 𝑙 could be
zero or one.
The question tells us that an
electron has a subsidiary quantum number of one, indicating that the electron is
found in a p-type subshell. Subshells consist of orbitals that
each have a different orientation. The individual orbital or
orientation can be indicated using the magnetic quantum number represented by 𝑚
subscript 𝑙. The possible values of the magnetic
quantum number depend on the subsidiary quantum number. 𝑚 subscript 𝑙 can be any integer
from negative 𝑙 to positive 𝑙. So when the subsidiary quantum
number is equal to one, the magnetic quantum number can be negative one, zero, or
positive one. These three values represent the
three types of p orbital contained in a p-type subshell.
The question asks how many
different orbitals the described electron could be in. We know that a p-type subshell
contains three different orbitals. So an electron with a principal
quantum number of two and a subsidiary quantum number of one could be found in three