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Consider an electron in hydrogen having total energy $- 0.5440 \mathrm { eV } .$ (a) What are the possible values of its orbital angular momentum (in terms of $\hbar$ ? (b) What wavelength of light would it take to excite this electron to the next higher shell? Is this photon visible to humans?

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(a) $\sqrt{20} \hbar$(b) 7470 $\mathrm{nm}$

Physics 103

Chapter 29

Atoms, Molecules, and Solids

Atomic Physics

Nuclear Physics

Cornell University

Rutgers, The State University of New Jersey

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.

01:38

Consider an electron in hy…

01:01

a. How much energy is need…

07:42

Predict/Calculate The elec…

05:40

An energetically excited h…

05:10

Consider a Bohr model of d…

Okay, So in this question, we know that an electron and hydrogen has an energy of 0.544 evey. And we also, um And we want to know, I guess. What are the possible values of orbital angular momentum? Well, we need to find the end the principal quantum number for this electron. And so we could do that based on information in the other chapter, the previous chapter which says that the energy levels in the hydrogen spectrum are negative 13.6 over and squared. So if we plug this in for E and sulphur and we would got unequal is five so that means that little Al can equal, um, 01234 all the way up to unwind this one. Um And so we want to get the possible values of orbital angular momentum in terms of age far. So we just wanna use this. L equals the square root of all times. L plus one. And so therefore, beach bar. And so the possible values R l If you plug in zero, he'll get zero. If you plug in one, you'll get the square root of two. And if you plug in to get square to six, um, people again. Three. You'll get the square to 12. Yeah, if you plug in four, you'll get the square root of 20. And then that's all in units of age bar. And then the next question is saying what wavelength to the next higher show. So that would be, um, so we want to find the current shells. What's the energy consuming? The final on current shell. So the final show would be an plus one. So that's, uh, 13 points extra out of my 36 minus the negative. 13.6 over the current over the current and which is five times five is critical is 25. And then we would set that energy difference equal Thio HC over lambda and sulfur lambda by cross multiply, for example. I'm gonna pause the video while I do that calculation. Okay, I got 7470 Nana meters. Um, and then that's much too large to be seen by humans. Humans, I think can see maybe up to, um maybe a little bit lesson. 1000 nanometers, um, by 56 is in the middle. Three 100 something maybe it's the lower. And so I would say that this is definitely you can't see it. Um, yeah, that's why I guess I'll just write down that answer. No. In visible.

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