You would like to observe an E. coli bacterium that is 1.85 yen long. Because di

Question

You would like to observe an E. coli bacterium that is 1.85 yen 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? What is the energy of an electron with a de Broglie wavelength of this size? In terms of energy, which particles, photons or electrons, are the least likely to damage your sensitive biological sample? photons electrons they are the same

Explanation / Answer

wavelength = 1.85 um = 1.85 x 10^-6 m

h = 6.63 x 10^-34 J s

a)

Energy of photon with this wavelength = h c / wavelength

= (6.63 x 10^-34 x 3 x 10^8 ) / (1.85 x 10^-6)

= 1.0751x 10 -19 J

b)

momentum , p = h / wavelength = (6.63 x 10^-34)/(1.85 x 10^-6) = 3.5838 x 10^-28 kg m/s

Energy of electron with this wavelength = 0.5 p^2 / m = 0.5 x ( 3.5838 x 10^-28 )^2 / (9.11 x 10^-31)

= 7.0491 x 10^-26 J

c)

Electron has lesser energy, they have least impact

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