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Problem 5 Medium Difficulty

The Balmer series for the hydrogen atom corresponds to electronic transitions that terminate in the state with quantum number $n=2$ as shown in Figure 42.2 and Active Figure $42.8 .$ (a) Consider the photon of longest wavelength. Determine its energy and wavelength. (b) Consider the spectral line of shortest wavelength. Find its photon energy and wavelength.

Answer

a. $E=1.89 \mathrm{eV}, \lambda=656 \mathrm{nm}$
b.$E=3.40 \mathrm{eV}, \lambda= 365 \mathrm{nm}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Simon Fraser University

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Video Transcript

first question, we just fight the longer hours a shoulder swift length for our bomber Siri's. So we know that Bubba stories escape looking at transitions. That and with the final state, that any goes to to right. So starting from any end prime status equals or greater to tree don't to any question to. And what we're looking at is T we thank off the photons being emitted. So we were looking at the highest. Sorry, the largest possible wavelength. Remember that energy or the photo close to it? See overlap. So we're looking at the largest possible. We think she looking at this smaller possible energy off the fort. Once you get the smallest possible energy, get rights. And, uh, this for the bomber Siri's. This month's possible energy get will be between, and it goes to a tree and articles to to. So basically we want toe Fine. What is this weakling off the photo coming down from medical treatment equals two energy or photo. In this case, we use the effect their energy off any states. It's negative 13.6 feet by end square. So I ask you one, you treat minus you too. Excellent. is the energy or the 4th 1 Okay, great to see overlap so sometime is close to it's just see over 1.9 you fee. Hey C can be written in another form, which is, boy it. See, you just have to putting the values. It's a conflict from E V into juice sa units. If you get a lot, we think to be about six 56 centimeters. So this is the longest possible with length football issues. Yet if you look at the shortest possible wavelength, so if you want this to be very, very small, it's a total energy must be very, very lunch, and the largest possible and she get all right would be when and prime music was to infinity, like the ionization energy level down too many close to two. So the energy or the photo on this case, the energy of the under section level. It's just cereal. My notes. Negative 2.6 to 2. Just treat my four CV. I want to get me to the same process, right? Because toe it's see over energy Photons. Try getting roughed out Boat 365 millimeters

National University of Singapore
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Farnaz M.

Simon Fraser University

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg