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Bragg Diffraction UncertaintyIn performing microwave diffraction activity detenmined that the spacing between the atoms Jiven by 4 J(2 sin €) . Assuming wavel...

Question

Bragg Diffraction UncertaintyIn performing microwave diffraction activity detenmined that the spacing between the atoms Jiven by 4 J(2 sin €) . Assuming wavelength of ^ 2.00 45.0" $ S1 what the uncertainty vour measured senaratian due the uncertainty vour measured angle? H41cMmeasured the peak angle t0 beIncorrect

Bragg Diffraction Uncertainty In performing microwave diffraction activity detenmined that the spacing between the atoms Jiven by 4 J(2 sin €) . Assuming wavelength of ^ 2.00 45.0" $ S1 what the uncertainty vour measured senaratian due the uncertainty vour measured angle? H41cM measured the peak angle t0 be Incorrect



Answers

A photon of wavelength $6000 \mathrm{~A}$ is passed throcigh a slit of widrh $0.2 \mathrm{~mm}$ (a) Calealate the uncertainty introduced in the angle of emcrgence. (b) The first minimum in the single slit diffraction pattem oceurs at $\sin ^{-1}(\lambda / b)$ where $b$ is the width of the slit. Culculate this angle and compure with the angle obtained in nart $(\mathrm{s})$

Okay now it's an easy question. We need to calculate the distance between the plans of atom responsible for deflection. So we've lint for X ray Is 1.54. I am strong. The diffraction is the first order hence, and an angle of diffraction hence N. And angle of diffraction. We will be 1.4-2 and the value of N is one using drugs equation and lambda equals two D. Sign Pito here is a very violent and angle of deflection. Pita. We can rearrange this equation E equals And is λ divided by two scientific. We substitute the respective values into the equation for D. It comes out one 1.54. I am strong, divided by two. Sign 14.22. And the distance between the plains of atom turns out to be 3.13. I'm strong.

This problem gives us the equation and Lambda equals two D signed Fada as well as the data Lambda equals 1.5. For an extra mes Fada equals 14.22 degrees and an equals one. And so we can plug in all these values. So we have one times 1.5 for an extra mes equals two d sign of 14.22 degrees and then we can solve for de to be 3.13 Angstrom Sze. And so this is the distance between layers off the material that caused this refraction of light. And this makes sense as a as a distance between layers, molecularly speaking.

In their study of x ray diffraction William and Lawrence Bragg determined that the relationship among the wavelength of radiation and the angle at which the radiation is distracted and the distance between the layers of the atoms in the crystal that caused the diffraction is given by the equation. In lamb. There were land as a wavelength equals two time's D. This is the distance time is a sign of data in question. A We're told x rays from a copper x ray tube have a wavelength of one point 54 the extremes and I saw this in PICO meters. Get it to a whole number using the brake equation and and equals one. Let's solve this equation and we're solving it for wavelength. Thank you. Let me go back and check here. Check one thing. Actually I'm solving for D. Here So this equals and is one 1:54 P Conveners Times two times the sine of theater and that was 0.2.5 Which equals 314 km, Which is 3.14 tanks drums in part B. Which I think I'm making this too easy. Were asked to do the same calculation except in equals two and everything else stays the same. Repeat the calculation but for any equals two. So for n equals two I've just got to there. So this will just be double that. I feel like that second part is wrong but I don't know what

And this problem we are asked to consider the work of William and Lawrence Bragg in their study of X ray diffraction. They determined the relationship among the wavelength of the radiation. Clammed up the angle with the with which the radiation is distracted data. And the distance between the layers of atoms in the crystal that caused the different that caused the diffraction D. And they say it's given by N. Lambda equals two D. Signed data. I'll write that all down. Okay, so that's everything we were given X rays from a copper x ray tube. I got to see if I'm gonna be able to fit all this in one page. Maybe I can. Yeah. Mhm. Okay. So there's the that's our whole question there. X rays from a copper X ray tube That have a wavelength of 1.54 angstrom are diffract id at an angle of 14.22° by crystal. Silicon We're going to use the Bragg equation above assuming n equals one. Just first ordered a fraction. We're going to calculate the inter planer spacing in the crystal. It's not as bad as you think because they've given us everything. It's just a southern salt. So I'll write the equation again over here and I'm gonna rearrange it for D because that's what we're solving for. So we get D equals lips and is one. So Our live web link was 1.54 extremes. Gonna divide that by two times the sine of 14.22. Do our math. We get three 135. And let's get that to three. Sig figs 3.14 Angstrom. That's our answer. Mhm. I guess I got to take this a little bit further. I have my mouth, I had it to one 3.1346 So I should go 3, 1 3 bangs drums and that's part A. Let's prepare for part B. These questions where I have to write so much to get the questions down. Drive me crazy. Be a shorter though. We're going to repeat a but this will be a second order diffraction diffraction that's and equals two. So that is as simple as you think basically double this. But I'll write it down And I got 6.269 6.27 Extremes upstairs. My answer right there in just a quick note. We just double this. We doubled by doubling and


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