Quantum Numbers: Nodes: Study with Video Lessons, Practice Problems & Examples

In quantum mechanics, understanding the electron's location within an atom is crucial, despite most of the atom being empty space. A node is a region where the probability of finding an electron is zero, indicating no electron density. Electron shells are areas with the highest likelihood of locating electrons. The total number of nodes in an atom is determined by subtracting one from the principal quantum number ($n$). Nodes are categorized as radial or angular nodes. Radial nodes are spherical regions separating different shells, with their number calculated by $n-l+1$. Angular nodes are flat planes or cones that divide orbitals and their quantity equals the angular momentum quantum number ($l$). Understanding these concepts is essential for grasping the structure and behavior of electrons in atoms.

Quantum Numbers: Nodes

With quantum mechanics, we're obsessed with finding the location of an electron, but just remember that a vast majority of the atom itself is empty space. Since the electrons are so small, we're going to say a node is the region within an atom with a probability of finding an electron is 0. We'd say that this region has zero electron density.

We're going to say electron shell is the region where electrons reside with highest probability, which is what we've been focusing on in terms of quantum mechanics. Now to determine the total number of nodes, just remember that it's equal to your principal quantum number n−1. If you know your principal quantum number for a given set of orbitals, subtract 1 and that be equal to the number of nodes.

Quantum Numbers: Nodes Example 1

How many total nodes are present in a 4D orbital? Now remember the total number of nodes is equal to n−1.

Since the number here is 4, that means we're dealing with electrons found within the 4th shell of an atom. So n=4.

So 4−1 would mean that we have 3 total nodes present within a 4D orbital.

Quantum Numbers: Nodes

Now a node can be further classified as either a radial node or angular node. Now a radial node is just the spherical region that separates the different shells. Here we have shell one which is n=1, shell 2 which is n=2, and then shell three. The space between them are your radial nodes and the number of radial nodes is equal to n-l+1.

Your angular node is are basically flat cones or planes that dissect the orbitals of an atom. So this is more 3 dimensional. Basically what you need to know here is that the number of angular nodes is equal to just l which is your angular momentum quantum number.

So we now know how to calculate the total number of nodes by n-1. Those total number of nodes can be further separated into either radial nodes or angular nodes. Here we have their formulas in purple boxes, which means it's U to you to memorize them.

Quantum Numbers: Nodes Example 2

Here we need to determine the number of radio nodes that exist for a 5F orbital. Remember the number of radio nodes is equal to N-L+1. Since the number of the orbital is five, that tells us it's in the 5th shell of an atom, so N=5.

Since the letter is F, that tells us what L is. Remember when the letter is F, our sub level letter, that means that L=3, so that L=3+1. So this comes out to 5-4, which means that there's only one radio node for a 5F orbital.

Which atomic orbital has the fewest angular nodes?  

• A. 3d
• B. 4p
• C. 7s
• D. 5d
• E. 6f

Which atomic orbital has the greatest number of radial nodes?

• A. 3s and 4s
• B. 4s and 6d
• C. 2p and 3s
• D. 6d and 4f
• E. 4f and 4s

Here’s what students ask on this topic:

What is a node in chemistry?

In chemistry, a node refers to a point or a plane within an atomic or molecular orbital where the probability of finding an electron is zero. Nodes can be of two types: radial and angular. Radial nodes are spherical surfaces around the nucleus where the electron density is zero, and they occur in s, p, d, and f orbitals as you move away from the nucleus. Angular nodes, on the other hand, are planes where the electron density is zero due to the shape of the orbital. For example, p orbitals have a dumbbell shape with a nodal plane at the nucleus, while d orbitals have more complex shapes with additional nodal planes.

The number of nodes in an orbital is related to its energy level and quantum numbers. As the principal quantum number, n, increases, the number of nodes also increases, indicating a higher energy orbital. Nodes are significant because they influence the chemical properties of atoms, such as the types of bonds they can form and their reactivity.