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handin08

# handin08 - Physics 212 Classical and Modern Physics Spring...

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Physics 212 Classical and Modern Physics Spring 2008 Solutions for Hand-In Set #8 A51 — Microscopes (a) No, it couldn’t. The reason is that light has wave- lengths in the 400 nm to 700 nm range, which is much larger than the virus. Sending visible light through a 10-nm slit would create strong diffraction, or bending of the light, and it does the same thing when encountering a 10-nm object. Some of you might be thinking, “But what if I use shorter wavelength light?” Certainly, you can get around the resolution problem by working with 1 nm light, so that diffraction effects aren’t a problem. How- ever, what’s the energy of a 1 nm photon? E ph = 1240 eV · nm 1 nm = 1240 eV This is way more energy than the typical binding energy for chemical bonds in biomolecules (see Problem A 52), so you’ll end up destroying the virus by illuminating it. (b) Let’s find the electron speed that will give a wave- length of 1 nm. By de Broglie we have p = h λ = 6 . 63 × 10 - 34 J · s 10 - 9 m = 6 . 63 × 10 - 25 kg · m/s Now use p = mv to find v = p m = 6 . 63 × 10 - 25 kg · m/s 9 . 11 × 10 - 31 kg = 7 . 28 × 10 5 m/s The energy of these electrons is considerably smaller than the energy of 1 nm photons, and so this is a much less destructive way to image at 1 nm resolution.

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