The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a) What is the quantum number l for this orbital?

Question

Contour representation of a n=3 hydrogen atom orbital, illustrating angular momentum quantum number.

Accepted Answer

Welcome back everyone in this example we need to determine the value of the quantum number. L. For the given representation of an orbital where the orbital lies at the fourth energy level. So this is the representation of our orbital given in the prompt and we should recognize that we have a dumbbell shape that is surrounded buy a ring whenever we have an orbital with the shape described here, we would recall that this is for a D. Orbital. Recall that we can also depict the orbital's as a flower shape. So the orbital's can also be depicted as a flower shape where we have four lobes which intersect one another and form a flower shape here. So this is just a small sketch of how you can also recognize a D. Orbital. But in this case we're given the dumbbell shape surrounded by ring. So we know we have a D. Orbital here and it lies at the fourth energy level according to our prompt. Now we want to recall our facts on quantum numbers and given in the prompt we have a value of N being four which is our energy level here for orbital. And we should recall that and is also known as our principal quantum number. And according to the prompt because we need to find L. Recall that L. Is known as the angular momentum quantum number. Now you can determine the angular momentum quantum number by taking your principle quantum number N. And subtracting it from one which would give you a range of L. Values which in this case would be for N - or sorry for - and that would give us L equal to either values of 01, two or three. However, because we are given specifically the representation of a D orbital, we can say that because we have a D orbital given we can say therefore our value for L is always going to equal for a D orbital the value to and that is because a angular momentum quantum number with a value of two corresponds to a D orbital. And so our final answer to complete this example is going to be that L is equal to two. So what's highlighted in yellow in our solution is our final answer here. If you have any questions, please leave them down below and I will see everyone in the next practice video.

The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (a) What is the quantum number l for this orbital?

Verified Solution

Key Concepts

Quantum Numbers

Angular Momentum Quantum Number (l)

Orbital Shapes