The resolution limit of a microscope is roughly equal to the wavelength of light used in producing the image. Electron microscopes use an electron beam (in place of photons) to produce much higher resolution images, about 0.20 nm in modern instruments. Assuming that the resolution of an electron microscope is equal to the de Broglie wavelength of the electrons used, to what speed must the electrons be accelerated to obtain a resolution of 0.20 nm?

Video transcript

Hey everyone, we're asked to determine the velocity of a proton. If it has a wavelength of 350 PICO meters to answer this question, we need to recall the formula of wavelength equals plank's constant, all over mass, times velocity. And since our question asked for a velocity of a proton, we need to remember that the mass of a proton Is equivalent to 1.67 times 10 to the -27 kg. Now, let's go ahead and plug in our values. So our wavelength is equivalent to Plank's constant, which is 6.626 times 10 to the negative kilograms times meters squared over second. And we're going to divide this by our mass of a proton which is 1.67 times 10 to the -27 kg. And we're going to multiply that by its velocity of 350 times 10 to the negative 12 m since a peak zero m is going to be 10 to the -12. When we calculate this out, we end up with a value of 1.13 times 10 to the 3rd m/s. And this is our final answer. So I hope that made sense. And let us know if you have any questions