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Consider an electron in the $N$ shell. (a) What is the smallest orbital angular momentum it could have? (b) What is the largest orbital angular momentum it could have? Express your answers in terms of $\hbar$ and in SI units. (c) What is the largest orbital angular momentum this electron could have in any chosen direction? Express your answers in terms of $\hbar$ and in SI units. (d) What is the largest spin angular momentum this electron could have in any chosen direction? Express your answers in terms of $\hbar$ and in SI units. (e) For the electron in part (c), what is the ratio of its spin angular momentum in the $z$ direction to its orbital angular momentum in the $z$ direction?

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(a) 0(b) $3.65 \times 10^{-34} \mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}$(c) $3.16 \times 10^{-34} \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$(d) $5.27 \times 10^{-35} \mathrm{kg} . \mathrm{m}^{2} / \mathrm{s}$(e) 0.167

Physics 103

Chapter 29

Atoms, Molecules, and Solids

Atomic Physics

Nuclear Physics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

University of Winnipeg

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.

06:27

Consider an electron in th…

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11:19

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04:32

Consider an electron in t…

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(a) Show all the distinct …

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(a) What is the lowest pos…

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02:23

Compute the ratio $S / L$ …

06:46

An electron in an atom has…

Hey, so when this problem, we're concerned with an electron in the end show. So if it's in the big and shell from, that means if little and principal quantum number is equal to four. And first we're concerned with what is the smallest orbital angular momentum. So if it's unequal is fourth, and that means it's El is equal goes from 0 to 4. So how those pathetic goes from zero Sorry, 0 to 3, and that means the smallest, elegant little Ella could have a zero. And since Big L is calculated by calculating AL times, L plus one, if you click in Little Al equal zero here you get zero. And so that's a concern for A. And for B, we're concerned with largest angular, orbital, angular momentum it could have. So a zay said before a little Al goes up to three. So Big Al can go up to the square root of three times, for which is 12 um, each far, and then putting that in s i u nits. I got that. That's equal to 3.64 times 10 to the minus 34 Jule second and for C, we want to know, Um, largest, um, a mug around England remind of the longest in direction. So, um, so even though the magnitude of l could be up to this amount along a certain direction like I eat a Z projection, it could only have the, um L Z, which is in the biggest LZ it can have is three h bar. So if I evaluate three times HPR Oh, my God. Um, you one second, can you just do that on my hot? Actually, 3.15 times. 10 to the minus 34 Um, and then for a d. So we want to get the largest spin angular momentum. So because it's a spin half particle, um, the largest mind issues spin is gonna be the square root of three over to when this is talked about in the book Times Age bar. And then if we put that into S I units, we got 9.9 times 10 to the minus 35 drool second and for E. We want to get the ratio spend too orbital, angular momentum. So we want to take this spin in this interaction divided by l Z. Um, and then so in for the electrons in C l c'est three. So it's ah, three h bar and then spend is equal to 1/2 age bar, and so this ratio can go up. Thio, um, 0.167 groups not one sexy 16 seven.

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