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Problem 23 Easy Difficulty

X-rays of wavelength 0.140 $\mathrm{nm}$ are reflected from a certain crystal, and the first-order maximum occurs at an angle of $14.4^{\circ} .$ What value does this give for the interplanar spacing of
the crystal?

Answer

0.281 \mathrm{nm}

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Top Physics 103 Educators
Marshall S.

University of Washington

Farnaz M.

Other Schools

Zachary M.

Hope College

Aspen F.

University of Sheffield

Video Transcript

Okay, So for this problem, we know that the wavelengths of the X rays or 0.1 for Indiana meters. Whoops. I got really excited about writing that for, but I snuck that one in there, and, um, the angle is 14.4 degrees. So, um oops. Almost wrote signe data. So the data is 14.4 degrees. So let's get that down. And we want to get the interpreter spacing. So we're gonna want to use Brax Law. Um, that describes position of the angular position of the peaks related to the crystal space, seeing as well as the wavelength. So that some Lambda a miss equal to one. I think it's just the 1st 1 First order? Yep. And so D is going to be equal to Landover to science data. So if we plug in data here and then Lambda, let's see what we get. So 0.14 times kind of them minus nine, all the right ID by two times the sign of was a 14.4. Yes. So with that, I got 2.81 times 10 to the minus 10 meters. Yeah,

University of Washington
Top Physics 103 Educators
Marshall S.

University of Washington

Farnaz M.

Other Schools

Zachary M.

Hope College

Aspen F.

University of Sheffield