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Problem 44 Hard Difficulty

An x-ray tube is operated at $5.00 \times 10^{4} \mathrm{V}$ (a) Find the minimum wavelength of the radiation emitted by this tube. (b) If the radiation is directed at a crystal, the first-order maximum
in the reflected radiation occurs when the grazing angle is $2.5^{\circ} .$ What is the spacing between reflecting planes in the crystal?

Answer

a. 2.49 \times 10^{-11} \mathrm{m}
b. 0.29 \mathrm{nm}

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

okay with this problem, we have an X ray to with operated it 50,000 volts and way Want to get the wavelength admitted by this too? And so to do that, we want to set the energy given by the change in voltage equal to the energy of of, uh, photons emitted. So we want to do Q b is equal Thio the energy photons. So each see over lambda and then well, exactly. We're resolving for wavelength so that lambda is full teach See divided by Q b m In plugging all of that into a calculator cues the charge of an electron. Just ask. Constancy is the speed of light I am getting. How many six picture include There is very sick I could do to point for eight times 10 to the minus 11 meters, huh? Not sure if I just stopped learning motor skills. I struggle still with this tablet. Maybe I should just try to go really slow. I don't like it. Go so slow them Okay anyway, So that's a And let's see what he is So and B, we want it's directed at a crystal. We want the first order Max when the grazing angle is 2.5 degrees I menopausal. I remember I review the formula with respect to that angle referred to with it. Okay, So the relevant formula for this is that to DIY Science data equals at Lambda. So let's see what we have. We have Lambda and we're told that the angle What was it? 4.7 degrees, 2.5 degrees. There is 2.5 degrees in this formula. Specifically does refer to that crazy angle and d Is that what we want? Oh, yeah, D is what we want so G equals question Mark. So just manipulating this formula little check mark here d He's equal to m lambda, uh, divided by two times the sign of data and then Oh, Ama's it's a first order, so I'm is gonna be one. So can we have that? And I'm gonna take landed about about you sign data because the video I d'oh Okay, so I got, uh, 2.8 times 10 to the minus 10 leaders. And is there anything else

University of Washington
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Marshall S.

University of Washington

Zachary M.

Hope College

Meghan M.

McMaster University