For crystal diffraction experiments (discussed in Section 39.1), wavelengths on the order of 0.20 nm are often appropriate. Find the energy in electron volts for a particle with this wavelength if the particle is (a) a photon.

Video transcript

Hey everyone. So this problem is about wave particle duality. And it's a pretty straightforward question. Pretty straightforward solution. We just need to recall a few key things. So let's see what it's asking us for. What is the energy and electron volts of an X ray photon used in dental radiography? If it has a 0.25 nanometer wavelength. Okay, so the first thing we need to do is recall the energy of a photon. In terms of wavelength, that equation is H. C. Over lambda where H is Planck's constant. So that's six, recall that 6.63 times 10 to the minus 34 jewel seconds. C. Is the speed of light. So recall it. That is three times 10 to the eight m per second. And then from the problem we are given that the wavelength lambda is 0.25. So nanometers that's times tend to be negative nine meters. And from there, it's just a bug and chug. Very straightforward. 6.63 times 10 to the negative 34 jewel seconds multiply that times the speed of light Three times 10 to the 8th m/s. And then our wavelength is 0.25 times 10 to the -9 m. Okay, so that gives us we plugged that in 7.96 times 10 to the -16 jules. But wait a second they asked us for energy in electron volts. So you're not going to find this answer in the choices. So the last thing we need to recall is that one electron volt is equal to 1.6 oh two times 10 to the negative 19 jewels. So we're gonna use that conversion factor multiply that by our answer in jewels to get our answer in electron volts. So that is 4.97 times 10 to the third electron volts. And again some unit conversion here, uh, 10 to the third electron volts is the same thing as a killer killer electron. So that is our final answer. 4.97 killer electron volts. And that would be answer seed. That's all for this problem. We'll see you in the next video.