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An electron in hydrogen is in the 5$f$ state. (a) Find the largest possible value of the $z$ component of its angular momentum. (b) Show that for the electron in part (a), the corresponding $x$ and $y$ components of its angular momentum satisfy the equation $\sqrt { L _ { x } ^ { 2 } + L _ { y } ^ { 2 } } = \hbar \sqrt { 3 }$

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(a) 3$\hbar$(b) $\sqrt{L_{x}^{2}+L_{y}^{2}}=\sqrt{3} \hbar$

Physics 103

Chapter 29

Atoms, Molecules, and Solids

Atomic Physics

Nuclear Physics

Rutgers, The State University of New Jersey

University of Washington

University of Sheffield

Lectures

02:42

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. The theory of quantum mechanics, a set of mathematical rules that describe the behaviour of matter and its interactions, provides a good model for the description of atomic structure and properties.

02:26

In physics, nuclear physics is the field of physics that studies the constituents and interactions of atomic nuclei. The most commonly known applications of nuclear physics are nuclear power generation and nuclear weapons technology, but the research has provided application in many fields, including those in nuclear medicine and magnetic resonance imaging, ion implantation in materials engineering, and radiocarbon dating in geology and archaeology.

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An electron in hydrogen is…

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A hydrogen atom is in the …

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A hydrogen atom is in its …

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For an electron in a hydro…

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An electron is in the N sh…

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The maximum possible angul…

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A hydrogen atom is in an $…

given the set up in problem number 40. We haven't electrons in the five F State for part A. We want to find the largest possible value of the Z component of a tender moment. Well, for the five f st that means that our l is he got three and our Z component L Z is simply equal to in El Times each bar. That's terribly Bob. Let's try that again. And l can go from minus l all the way through zero up to cause it of El So you can say it goes from zero to plus or minus l and thus if we want to find the large possible value that yeah, we can get is when ml peaceful three. Who does r l Z is equal to We'll stay positive just to be clear. Three h bar. So not too tricky, all things considered, and then for part B, we want to show that this electron ah, the X and why components of that and get the momentum satisfy the equation given in the problem. Well, we have a another page here. We know that our total l is equal to the sum of the components squared This just a little simple vector manipulation. And we have what our LZ is already. So then we can We're sorry. We have what are Ellis and RLC? So we can move some things around just ever so slightly. If we write down our known l value here or else square, then let's move L z here over to the other side and we get the relationship that l X squared. Plus Il y squared is equal to l squared minus l z squared. And then finally l Z squared from the previous page. It is three h bar squared, so you get 12 h bar squared minus nine h bar squared, giving us a relation for l X squared plus l. Why squared being equal Tio square root of three time's a bar And that is exactly what is given in the problem.

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