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Problem 63 Hard Difficulty

(a) For a given value of the principal quantum number $n$ for a hydrogen atom, how many values of the orbital quantum number $\ell$
are possible? (b) For a given value of $\ell$ how many values of the orbital magnetic quantum number $m_{c}$ are possible? (c) For a given
value of $n,$ how many values of $m_{\ell}$ are possible?

Answer

(a) 1
(b) $2 l+1$
(c) $n^{2}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Meghan M.

McMaster University

Video Transcript

for about a off the problem they loved venues off l forgiven End are 012 up to n minus one. Thus, there are in different values off l but be they loved values for off ml for the even. L you are minus l minus. So minus tell plus one up to, uh, l does. There are two l plus one different values off off M l What's she, um, according to part a above. For a given in, there are n different values off l Also each off, these else can have to l plus one different values off m l. That's the total number off ML is then given by some off are elves from zero to end, minus one into two l plus one that isn't going to end square.

Wesleyan University
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Meghan M.

McMaster University