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Problem 20 Easy Difficulty

When x-rays of wavelength of 0.129 $\mathrm{nm}$ are incident on the surface of a crystal having a structure similar to that of NaCl, a first-order maximum is observed at $8.15^{\circ} .$ Calculate the interplanar spacing of the crystal based on this information.

Answer

0.455 \mathrm{nm}

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Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Zachary M.

Hope College

Video Transcript

Okay, So for this question, we know X rays were admitted and they have a wavelength. Appoint 1 to 9 centimeters. Let's go ahead. Write that town. Lambda is point 1 to 9 times 10 to the minus nine meters. And we want what we want. Um, we know that there's a max at 8.15 degrees. We want to get the inter cellular spacing, So data equals 1.85 degrees and, um, then inflate your spacing. So what we want to do is, um, use the brags law equation. Um, and so that says that two D signed data is I'm Lambda. Let's go ahead and write that down and I'll go over what each thing means. Um so d is the spacing. So that's what we're looking for. Ama's the order. So So they said for stores, That's one. And then here's our Landa. Um and so, yeah, in order for tick up the constructive interference. This this needs to be satisfied. So I'm gonna go ahead and plug everything in and then solve for Dee Dee is equal to Lambda over to sign they Ah, and then I'll plug in Data and Lambda so I'm gonna possibly all I do that. Okay, I got 4.55 times, 10 to the minus 10. And, um, I also meters, and I also realized that I didn't transcribe this angle properly. I wrote 1.5 originally, but it's 8.15

University of Washington
Top Physics 103 Educators
Elyse G.

Cornell University

Andy C.

University of Michigan - Ann Arbor

LB
Liev B.

Numerade Educator

Zachary M.

Hope College