Quantum Numbers: Principal Quantum Number: Videos & Practice Problems

The principal quantum number ($n$) is fundamental in understanding atomic structure, as it defines the size and energy level of an atomic orbital. As $n$ increases, so does the size and energy of the orbital. This quantum number is directly tied to the periods or rows of the periodic table, with each shell corresponding to a specific period. Currently, there are seven periods, reflecting our current technological capabilities in discovering or synthesizing new elements. However, this is not a fixed number; as technology advances, we could potentially discover or create elements that would expand the periodic table beyond seven periods. The principal quantum number must be an integer starting from one and, theoretically, can extend to infinity, indicating that there could be an infinite number of periods in the future. Understanding $n$'s role is crucial for comprehending how electrons are arranged in atoms and their subsequent chemical behavior.

Principal Quantum Number

The first quantum number of interest is the principal quantum number. It uses the variable N and the principal quantum number deals with the size of the shell, and the size of a shell is equal to the energy level of that shell. What we need to realize here is the value of N increases, then both the size and energy level of an atomic orbital will also increase.

Now we're going to say here that the energy levels, or shell numbers of an atom can be tied to the periods or roles of the periodic table. So here we take a look at an atom. Here we have our nucleus in the middle. We have here our first shell, so N=1 all the way to our 7th shell here, which is N=7. These shell numbers are connected to the periods or rows of the periodic table. So shell one is connected to. One and as you can see we want all the way up to to shell 7. And looking at the periodic table, we have periods 1 to seven.

Now here's the thing, the periodic table, if you've watched my videos on it, we know that the periodic table is not a static thing, meaning that it's not going to stay in this form forever. In fact. 7, a lot of those elements in. Seven were only discovered within the past century. That's because as we explore new places on Earth, as we explore the universe, as our technology becomes more advanced, we'll discover new elements, we'll create new elements. So theoretically, the number of rows in the periodic table is infinite. Right now we have 7 rows, but it can increase to 8 rows, 10 rows in 1000 years.

So just realize here that the number of rows for the periodic table doesn't stop at 7, it's only 7. Now because of where we are technologically. In the future there's going to be more than 7 rows, so we're going to find atoms that go beyond seven. This ties into the limitation of the principal quantum number. We're going to say here that the principal quantum number N must be an integer, so a whole number. And since it's connected to the periods of the periodic table, it has to start off at one at the lowest as its lowest possible value.

And we just said that the number of rows is not static, it increases over time. So N theoretically can be any whole number from one to Infinity. So I just realized that on an exam or a quiz you see n=22. That's possible, we just haven't gotten there yet. So just remember the principle quantum number is connected to the size and energy of a shell and it affects the size and energy of the orbitals.

Principal Quantum Number Example

Here in this example question it says which of the following is a possible value for a principal quantum number shell. So here we have N equals -3, negative 4011 and -7. Remember we said that your principal quantum number north is connected to the periods or rows of the periodic table. The smallest. Value we can have a row is 1.

And we said that the periodic table is dynamic. It's always increasing. Right now we have 7 rows, but in the future we're going to we're going to have 8910 rows. It can continue onward. So here theoretically N equals any value from one to Infinity. That means all these negative values would not work, and N cannot equal 0 has to start off as one as a possible value.

So the answer here would have to be option D Theoretically N can equal 11.

What is the value of n for the electron based on the image of the atom provided?
 

• A. n = 3
• B. n = 5
• C. n = 1
• D. n = 2
• E. n = 6

Answer: (D)

Which electron possesses the lowest possible energy from the image provided?

• A. A
• B. B
• C. C
• D. D
• E. E

Answer: (D)

Here’s what students ask on this topic:

What is the principal quantum number?

The principal quantum number, denoted as n, is a quantum number that specifies the energy level of an electron in an atom. It is one of four quantum numbers which describe the unique quantum state of an electron. The principal quantum number can take any positive integer value ($n=1,2,3,\dots$), and as it increases, it indicates an electron is in a higher energy level, or shell, further away from the nucleus.

The energy associated with each level increases as n increases. This means that electrons in higher principal quantum numbers are less tightly bound to the nucleus and have higher potential energy. In addition, the principal quantum number also determines the number of subshells available within a given shell, and thus, the maximum number of electrons that can occupy that shell. For example, for $n=2$, there are two subshells (2s and 2p), which can hold a total of 8 electrons. The principal quantum number is fundamental in understanding the electronic structure of atoms and the arrangement of electrons in various atomic orbitals.

What does the principal quantum number determine?

The principal quantum number, denoted as n, is a quantum number that fundamentally determines the energy level of an electron in an atom. It is an integer that can take on any positive value ($n=1,2,3,\dots$). The larger the value of n, the higher the energy level and the larger the orbit or shell in which the electron resides. As n increases, the electron can be found further from the nucleus, which means that the electron has a higher potential energy and is less tightly bound to the nucleus. This quantum number also indirectly influences other properties of the electron such as its orbital size and the number of possible subshells within a given energy level. For example, for $n=2$, there can be s and p subshells, leading to different shapes and orientations of the electron orbitals.

How can I find the principal quantum number?

The principal quantum number, often symbolized as n, is one of the four quantum numbers which describe the unique quantum state of an electron in an atom. It essentially defines the electron's shell or energy level. To find the principal quantum number, you need to look at the electron configuration of the atom or ion in question.

For instance, if you're considering a neutral atom of carbon, its electron configuration is 1s² 2s² 2p². The highest value of n in this configuration is 2, which means the outermost electrons of carbon are in the second energy level.

The principal quantum number n can take any positive integer value starting from 1 upwards. The larger the value of n, the higher the energy level and the farther the electron is from the nucleus, on average. Each energy level can hold up to 2n² electrons. So, you can determine n by looking at the period (row) of the element in the periodic table or by counting the energy levels in the electron configuration.