Quantum Numbers: Number of Electrons: Study with Video Lessons, Practice Problems & Examples

Atoms are structured with electron shells, where each shell has a capacity determined by the formula:

$2n^2$

where 'n' is the shell number. For instance, the first shell (n=1) can hold up to 2 electrons, and the second shell (n=2) can accommodate 8. Beyond the shell number, electrons are further organized into orbitals based on quantum numbers. Each orbital can host a maximum of 2 electrons. The quantum number 'l' indicates the type of orbital, which directly relates to the number of orbitals available. By knowing the 'l' value or sublevel letter, one can calculate the number of orbitals, and thus the total number of electrons by doubling the orbital count. Additionally, the principal quantum number 'n' can be used to find all possible 'l' values by calculating:

$n-1$

which then leads to determining the total electron count. Understanding this hierarchical structure is crucial for grasping how electrons are distributed within an atom.

Quantum Numbers: Number of Electrons

Now remember, an atom possesses shells. Each shell for a given atom has a maximum number of electrons it can hold. Here, when only the shell number n is given, the number of electrons is equal to two times n squared.

So if we're looking here at the first shell where n = 1, that would mean that we have 2×12, which is 2×1. So the first shell can hold a maximum of two electrons. The second shell here n = 2, that'd be 2×22 which would be 2×4 which equals 8 electrons max that it can hold.

So remember if they only give you the n value, then you can use two times n squared to determine the total number of electrons found within that given shell.

Quantum Numbers: Number of Electrons Example 1

Here we have to determine how many electrons can be found in the 7th shell of an atom. So remember 7th shell corresponds to n=7 when we only know the shell number. The number of electrons is just equal to 2∗n2, so that would equal 2∗72.

72 is 49, and multiplying it by two means that we can have theoretically up to 98 electrons within the 7th shell of a given atom. So that would mean that option D would be our correct answer.

Quantum Numbers: Number of Electrons

When we have more than just the quantum number n being given to us, then we must follow this quantum electrons road map O. The way it works is they could give us the l value for our electrons and if we know our l value of our electrons we can go straight into the number of orbitals involved. Remember each orbital can hold a total of 2 electrons, right? So one up and one down and then all we need to do is from the number of orbitals determine the number of electrons.

So since each orbital can hold 2 electrons, we multiply the number of orbitals by two and that will give us our number of electrons. Now they could also give you the sub level letter and that would correspond still to my l value and then you would take the same path you have your l value. From there you can determine the number of orbitals by ml. Remember ml is the range of l. Once you know your orbitals, multiply it by two to get the number of electrons.

Now what else could they do? Well they could give you your n value here and if you know the n value would do n-1 which would give you all the possible values of l and again knowing the l value would give you your ml value. Multiplying that by two would again give you the total number of electrons. It can be a bit complicated, but click on the next video and let's take a look at an example and how we're going to utilize this quantum electrons road map.

Quantum Numbers: Number of Electrons Example 2

Here it says determine the number of electrons that can be found in the 7th shell and D sub level. So step one tells me to determine the L value for either a given N value or from a sub shell or sublevel letter. Here they're telling me that it's D because it's D That means that we know that L is going to be two.

If they're just giving me an N value and some other quantum numbers, then I would have utilized this part of our map. Now we know L is equal to two if M sub L is not given. Use the L value to determine the number of orbitals. Remember M sub L is the range of L so M sub L would be -2 to two. So -2, -1, 0, +1, and +2.

That is a total of 5 orbitals and then based on the number of orbitals, find the number of electrons. Remember each orbital can hold a maximum of two electrons. If I multiply this by two, that means that I have 10 electrons that would be in the 7th shell and have a D sublevel letter.

Determine the number of electrons that can have the following set of quantum numbers:n = 3, m_l = 0.

• A. 2 e^-
• B. 4 e^-
• C. 6 e^-
• D. 3 e^-

Determine the number of electrons that can have the following set of quantum numbers:n = 2, m_s = –1/2.

• A. 2 e^-
• B. 4 e^-
• C. 6 e^-
• D. 3 e^-

Determine the number of electrons that can have the following set of quantum numbers.

n = 4, l = 3,  m_l = – 1

• A. 2 e^-
• B. 4 e^-
• C. 6 e^-
• D. 3 e^-

Determine the number of electrons that can have the following set of quantum numbers.

n = 4, m_L = – 1, m_s = –1/2

• A. 2 e^-
• B. 4 e^-
• C. 6 e^-
• D. 3 e^-

Here’s what students ask on this topic:

What is the maximum number of electrons that can be found in an individual orbital?

An individual orbital can hold a maximum of two electrons. This is due to the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of four quantum numbers. Since an orbital is described by three quantum numbers (the principal quantum number, the azimuthal quantum number, and the magnetic quantum number), the fourth quantum number, which is the spin quantum number, can only have two values: +1/2 and -1/2, representing the two possible spin states of an electron. Therefore, only two electrons with opposite spins can occupy the same orbital. This rule applies to all types of orbitals (s, p, d, and f) within an atom.

What is the maximum number of electrons in an orbital of any atom?

An orbital in an atom can hold a maximum of two electrons. This is due to the Pauli Exclusion Principle, which states that no two electrons in an atom can have the same set of four quantum numbers. Since an orbital is defined by three quantum numbers (n, l, and m_l), the fourth quantum number, which is the spin (m_s), can only have two values: +1/2 or -1/2. This means that only two electrons, each with opposite spins, can occupy the same orbital at any given time. This rule applies across all elements in the periodic table and is fundamental to the structure of electron shells and subshells in atomic physics and chemistry.