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$\bullet$ Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon energy for the $\mathrm{H}_{\gamma}$ line of the Balmer series for hydrogen.

A) 434 $\mathrm{nm}$

B) $6.91 \times 10^{14} \mathrm{Hz}$

C) 2.86 $\mathrm{eV}$

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University of Michigan - Ann Arbor

University of Washington

Simon Fraser University

Hope College

Okay, So for this problem, we're trying to calculate the wavelength pregnancy Proton energy for the gamma line of the bomber Siri's. So I wonder. Afraid you two figure 28.8 where it actually shows the bomber Siri's and then right below it there is the formula for the bomber syriza that corresponds to, um going thio the unequal to level from some higher level. And you can count that the gamma is the 5th 1 So, um because like, the 1st 1 is alpha's, that must be from one above to just three betas for Gammas five. You can also see from the figure to you that it has the, um Oh, that It just, like, tells you what the wavelength is, but I'll go ahead and calculate it or I mean, all right, down how to calculate it. So, um, you want to do one over Lambda is equal to our times. One over two squared minus one over on squared. And yeah, I mean, so Lamda is just this whole thing to the negative one, and you know, and I feel very confident that it will be 434 nano meters, so I will just go ahead and write that down. I guess I can also say the road burgh concert are is of the Redbird constant, um, whose value is one point? 097 times tend to the seven. And next. We want to get the frequency, so, uh, frequency is equal to Lambda over. See? Let's see. Is that right? Actually, meters, one of my meters per second out? No, you got in birth. That so it should be C over lambda. So I'm gonna go ahead and plug that into a calculator. So see, divided by 4 34 it was kind of the minus nine. And with that, I got 6.91 times 10 of the 14 hurts. And next, we want to get the energy. Energy is equal to h f. So, um, I will go ahead and plug in and multiply this af by h. And with that, I got 6.6266 66 times, 10 to the minus 34 I got, um, four point 58 times 10 to the minus 19. Jules. And then if you wanted to convert it

University of Washington