What is the maximum number of electrons in an atom that can
have the following quantum numbers? (a) n = 3, ml = -1;
(b) n = 4, l = 2; (c) n = 4, l = 3, ml = -2; (d) n = 5, l = 2,
ml = 0.

Question

What is the maximum number of electrons in an atom that can 
have the following quantum numbers? (a) n = 3, ml = -1; 
(b) n = 4, l = 2; (c) n = 4, l = 3, ml = -2; (d) n = 5, l = 2, 
ml = 0.

Accepted Answer

Hello everyone in this video we're given to quantum numbers and we're trying to see how many electrons can fit within these quantum numbers. So first let's not forget the kwame numbers. We have R N L. We have our M. L. And lastly the M. S. Alright so we're given and it goes to two and R N value is our principal quantum number. This serves as a kind of guide for the other numbers. So then let's move on to our L value. I'll values that give it to us. So we kind of have to look for that. So usually The L value is dependent on our end value because it ranges from zero 2, -1. We set the end, it goes to two here. So 02 let's see two minus one. That is one. So from 0 to 1. Alright. Our next number is our M S. For ml and RML is equal to zero and that is given to us. And usually the ml number is depending on the L number and it could be from arranging from negative L. They're positive since our M. L. Is given to us as zero and the M. L. Has to be within this range. Let's see here. So what number can be fit into or what else can be fit into here to give us zero? It's either going to be zero or 1. So we plug in one. This would either be -1 and positive one. However we can see here it's only zero. So this must be awesome. zero or Taliban. So let's go ahead and fill them in as helping syrup. And lastly, of course, r M s does not depend in any of the other three common numbers. So it can either be a negative half or positive health. All right, let's see here. So our M. S number is our spin number and can only have these two values. So our Ml can only have two M. S. S, which means that there can only be two electrons passed. So, I mean this rain is basically like saying this having zero and we know that only two electrons get fit in here and each electron will have one separate M. S number. So to formally answer this question, two possible electrons can be with the prime number of Andy goes to two And ML equaling zero. Let's go ahead and also highlight the as well. Alright, so this is going to be our final answer for this problem.

What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, ml = -1; (b) n = 4, l = 2; (c) n = 4, l = 3, ml = -2; (d) n = 5, l = 2, ml = 0.

Verified Solution

Key Concepts

Quantum Numbers

Electron Capacity of Orbitals

Allowed Combinations of Quantum Numbers