An X-ray beam with l = 154 pm incident on the surface of a crystal produced a maximum reflection at an angle of u = 28.3°. Assuming n = 1, calculate the separation between layers of atoms in the crystal.

Video transcript

Hey everyone in this example we're told that the maximum reflection of a UV light with a 315 nanometer incident on the surface of a crystal produced an angle of 26.4 degrees. We need to calculate the separation between layers of atoms in the crystal, assuming that these atoms are at the first energy level. So what we should recall is our following formula where we take our energy level, multiply it by the wavelength and we set this equal to two times the distance times sine of our angle data. However, we need to recognize that the separation between layers phrase here is referring to distance and we need to solve for distance. So we're going to reformat this formula solving for distance so that it's equal to our energy level times lambda, our wavelength divided by two times the sine of our angle theta. And so plugging in what we know from our prompt, we recall that The prompt tells us that we're at the first energy level. So we multiply one times our angle given in the prompt as nm. And then in our denominator we're going to have two times the sine of our angle which in the prompt is given to us as 26.4°. And so at this point we need to make sure that our calculators are in degree mode. So if you recognize that your calculator is in Radian mode. Just switch it to a degree and what we should get for our final answer is that this is equal to 354 nm, so this would be our final answer. To complete this example. I hope that everything I reviewed was clear, but if you have any questions, just leave them down below and I'll see everyone in the next practice video.