Video Transcript
What is the maximum number of electrons in a subshell with quantum numbers 𝑛 equals three and 𝑙 equals two? (A) Two electrons, (B) six electrons, (C) 10 electrons, or (D) 14 electrons.
To answer this question, we need to use the quantum numbers given to determine the maximum number of electrons that can occupy the described subshell. Electrons in an atom are located outside of the nucleus in various energy levels called shells. Each shell is composed of one or more different types of subshell that each have a slightly different energy. Subshells are composed of individual orbitals, and each orbital can contain a maximum of two electrons.
The shell, subshell, individual orbitals, and the two electrons each orbital can contain can be described using quantum numbers. There are four quantum numbers: 𝑛, 𝑙, 𝑚 subscript 𝑙, and 𝑚 subscript 𝑠. In the question, we are given a value for 𝑛 and 𝑙. So we’ll focus our attention on these two quantum numbers.
𝑛 is the principal quantum number. It represents the energy level or shell. It also determines the size of the orbitals. Orbitals in a shell with a higher principal quantum number have a larger radius than orbitals in a shell with a lower principal quantum number. Although the radius of an orbital increases with increasing principal quantum number, the maximum number of electrons an individual orbital can contain is two electrons regardless of the size of the orbital. So the principal quantum number cannot be used to determine the number of electrons a subshell can hold.
𝑙 is the subsidiary quantum number. It represents the type of subshell. There are a number of types of subshell, but four types are the most relevant. These subshells are denoted as s, p, d, and f. A subsidiary quantum number of zero corresponds to an s-type subshell, one to a p-type subshell, two to a d-type subshell, and three to an f-type subshell. We are told in the question that the subsidiary quantum number is two. So we know that the subshell in this question is a d-type subshell.
Now we need to determine how many orbitals this subshell contains. The total number of orbitals per subshell can be determined with the formula two times the subsidiary quantum number plus one. So a d-type subshell contains two times two plus one, or five orbitals. We have already established that each orbital can contain a maximum of two electrons. So, if each of the five orbitals can hold a maximum of two electrons each, then the subshell can contain a maximum of 10 electrons. Therefore, a subshell with quantum numbers of 𝑛 equals three and 𝑙 equals two can hold a maximum number of 10 electrons, or answer choice (C).
