Question Video: Determining How Many Electrons in an Atom Can Have a Principal Quantum Number of One Chemistry

What is the maximum number of electrons in an atom that can have the principal quantum number 𝑛 = 1?

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Video Transcript

What is the maximum number of electrons in an atom that can have the principal quantum number 𝑛 equals one?

Quantum numbers are values that can be used to completely describe an electron in an atom. There are four different quantum numbers: 𝑛, 𝑙, 𝑚 subscript 𝑙, and 𝑚 subscript 𝑠. The Pauling exclusion principle states that no two electrons in any one atom can have the same set of four quantum numbers. We need to use our understanding of quantum numbers and the Pauling exclusion principle to determine the maximum number of electrons in an atom that can have the principal quantum number of one.

The principal quantum number, represented by 𝑛, indicates the electron shell or energy level where an electron is found. 𝑛 can be any positive integer. In this question, we want to know how many electrons can have the principal quantum number of one.

The next quantum number is the subsidiary quantum number, represented by 𝑙. This quantum number represents the type of subshell or orbital shape. The possible values for the subsidiary quantum number depend on the principal quantum number. 𝑙 can have any integer value from zero to 𝑛 minus one. So, when 𝑛 equals one, 𝑙 can only have a value of zero.

The next quantum number is the magnetic quantum number, represented by 𝑚 subscript 𝑙. This quantum number indicates the individual orbitals in a subshell or the orbital orientation. The possible values for the magnetic quantum number depend on the subsidiary quantum number. 𝑚 subscript 𝑙 can be any integer from negative 𝑙 to zero to positive 𝑙. So, when 𝑙 is equal to zero, 𝑚 subscript 𝑙 can only be zero.

The final quantum number is the spin quantum number, represented by 𝑚 subscript 𝑠. This quantum number indicates the spin state of an electron. There are only two possible values for 𝑚 subscript 𝑠, positive one-half or negative one-half. So, for any value of 𝑚 subscript 𝑙, 𝑚 subscript 𝑠 could be negative one-half or positive one-half.

Let’s look at this information in another way. An 𝑛 of one represents the lowest energy level in an atom. This energy level or electron shell contains one subshell, 𝑙 equals zero. 𝑙 equals zero corresponds to an s-type subshell, which has a spherical shape. This subshell has one orbital or orientation, 𝑚 subscript 𝑙 equals zero. This orbital can hold a maximum of two electrons, one with a spin of positive one-half and the other with a spin of negative one-half. These two different perspectives confirm the correct answer.

Looking at the quantum numbers, we can see that there are only two possible combinations when 𝑛 equals one, signifying two different electrons. Looking at the energy levels and orbitals these quantum numbers represent, we can see that there are only two electrons that fit in the first energy level. So, the maximum number of electrons in an atom that can have the principal quantum number 𝑛 equals one is two electrons.