# Question Video: Determining How Many Orbitals an Electron Could Be In Given the Principal and Subsidiary Quantum Numbers Chemistry

An electron was found to have values of 𝑛 = 2 and 𝑙 = 1. How many different orbitals could this electron be in?

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### Video Transcript

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 different orbitals.