For each of the following sublevels, give the n and l values and the number of orbitals: (a) 6 g

step 1 Hi everyone, I'm here with Problem 58 from Chapter 7. In this problem, we're going to classify t

For each of the following sublevels, give the n and l values...

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Principal Quantum Number (n)

The principal quantum number indicates the energy level or shell in which an electron resides within an atom. It is a positive integer and determines the overall size and energy of the orbital, with larger numbers corresponding to electrons found further from the nucleus.

Azimuthal Quantum Number (l)

The azimuthal quantum number, also known as the orbital angular momentum quantum number, determines the shape of the orbital and is associated with the subshell type. Its value ranges from 0 to n-1 for a given principal quantum number, and each value corresponds to a specific subshell letter (for example, 0 for s, 1 for p, 2 for d, 3 for f, 4 for g, and so on).

Subshell Designation

Subshells are designated by letters (s, p, d, f, g, etc.) that correspond to specific azimuthal quantum numbers. This nomenclature helps in identifying the shape of the electron cloud and the angular momentum properties of the orbital.

Number of Orbitals in a Subshell

The number of orbitals available within a particular subshell is given by the formula 2l+1. This number reflects the different magnetic quantum numbers possible for a given azimuthal quantum number and determines how many electrons can potentially occupy that subshell according to the Pauli exclusion principle.

Transcript

00:01 Hi everyone, i'm here with problem 58 from chapter 7.

00:05 In this problem, we're going to classify the sub -levels you see on your screen by their n, l, and the number of orbitals.

00:15 So first, let's relate the sub -shell to your angular momentum quantum number, or l.

00:24 And by this, i'm referring to our s, p, d, and f.

00:38 So how do these relate to the number we're given for l? well, we know that if l equals 0, that corresponds to s, if l is equal to p, sorry, if l is equal to 1, we are equal to p, if l is equal to p, if l is equal to 2, that corresponds to d, and if l is equal to to 3 that is equal to f and so on.

01:24 So we can use this to figure out what sub -shell we are looking at.

01:30 So let's start with the first subshell 6g.

01:36 So we know n is our principal quantum number and that is the number that we see in our sub -shell.

01:45 So we know here n is equal to 6.

01:50 And next we want l.

01:53 So we just define each of our l's their sub -shells.

01:57 And this one is g.

02:00 We haven't defined g yet, but let's go ahead and define g.

02:04 So the next sub -shell would be l equals 4, and we know after f is the g subshell.

02:13 So now we know that for 6g, the angular momentum quantum number is 4.

02:24 And now we need to figure out the number of orbitals...