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When the principal quantum number is $n=4,$ how many different values of $(a) \ell$ and $(b) m_{\ell}$ are possible?

a) 4

b) 7

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Rutgers, The State University of New Jersey

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in this exercise. We have an atom at the fourth energy level and equals four. And in question A. We want to know how many different values of El that is. The orbital frontal number are possible. So remember that for a given end given energy level when he allowed, uh, L Z allowed orbital frontal numbers are ranged from zero to n minus one between. In this case, we have the possible else 012 and three. So in total, there are four allowed else. Okay, And for a question, be have to find Khomeini allowed magnetic quantum numbers. There are. Okay, so remember that for a given l the allowed magnetic quantum numbers range from minus l to l. So the largest l possible as we saw in question A is l equals three. Okay. And in that case, M l can be minus three minus two minus one zero one, two and three. Notice that in total there are seven. Okay. And this is this is the the number of allowed magnetic quantum numbers and else Okay, total there are seven. And this concludes the exercise

Universidade de Sao Paulo