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How many unique combinations of the quantum numbers $l$ and $m_{l}$ are there when (a) $n=3,$ (b) $n=4 ?$

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Carleton College

University of Central Florida

Numerade Educator

University of Maryland - University College

now we'LL discuss problem fifty six from chapter six. Come on. This problem asked us how many unique combinations of the quantum number l and M sub l are there when and is equal to three and is equal to four. So that's Irwin and is equal to three. You, if we're in the end, is equal to three orbital, then l could be equal to zero. It could be an s orbital could be ableto one. It could be a pure metal and it could be equal to two, which would be a D orbital. So for l is equal to zero. The possible values of M sub l R E r M Sobel is equal to zero. But if it's l is equal to one, If we're in a P orbital em Zobelle could equal negative one zero or one. And if we're in a the orbital l is equal to two hems. A bell could equal negative too negative one, zero, one or two. So that's all the possibilities of Ellen Upset Bell and that gives us a total of nine possibilities for part B. We're asked and is equal to four. So we're gonna have the same possibilities. Hell is equal to zero. L is equal to one. L is equal to two. But the difference now is that we could have a legal tow. Three. Excuse me. Ah, which would be in F orbital. And then from there we have the same values. M Zobelle could be zero for l equals zero. Could be negative. One zero or one for l'm. Cybele for l equals one for l equals to M. Isabel. Could be negative of two. Native one zero one or two and then for Ellis Eagle two three, we have the same thing. Negative three. Negative to native. One zero one, two and three. So we had nine before and we had had having addition of seven new possibilities. So here we have a total possibility of sixteen sets of quantum

University of Miami

Electronic Structure