Question

You would like to observe an E. coli bacterium that is 1.95 um long. Because diffraction blurs an image, you would like to minimize the effects of diffraction by using a wavelength no larger than the object you are observing. For this problem, assume the wavelength is equal to the length of the bacterium. What is the energy of a photon with this wavelength? energy of photon: J What is the energy of an electron with a de Broglie wavelength of this size? energy of electron: J In terms of energy, which particles, photons or electrons, are the least likely to damage your sensitive biological sample? electrons they are the same photons

Answer 1

to size of 2 constant • since, wavcungth of photon must be equal E. coli bacterium, we can take d=1.95 um Energy of photon, E = ho h= blanck E = 6.6*10 36 0 X 3x10 c = speed 1.95 x 10-6 of light = 10.15 x 10 T -19 J Energy of photon , t = 1.01 X10 8 -20 • of electron has this le-broglie wavelength, de = 1.95 HM If Ee is Ee is energy of electron, then By De-Brogue's formula, de Pame ſamte

2 2 Gior de amte 2 amfe de 2 62 6.6 xlo Fe = ande? -34 -34 X 6.6 x 10 -12 2x 9.1 810-31x1.95x1.95 x 10 -25 0.6294 x 10 J - 26 Energy of electron = 6.3 X10 4

Electron since energy of electron is much less than photon for same size, electron is least lilcery to damage the biological sample.