The best resolution you can get (that is, the smallest object you can distinguis
ID: 1428332 • Letter: T
Question
The best resolution you can get (that is, the smallest object you can distinguish) for any microscope is about half of the wavelength of the light (or other wave) you are using. (a) Calculate the size of smallest object we can distinguish with light in the visible spectrum. (b) In an electron microscope, electrons are emitted at speeds of 7.5 × 106 m/s. At this speed, what is the momentum of one electron? (electron mass = 9.11 × 1031 kg) (c) What is the de Broglie wavelength of the electron in part (b)? (d) What is the size of the smallest object that this electron microscope can distinguish?
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Since red is 700 nm, and its the smallest visible light does this mean the smallest object would have to reflect 350 nm? I'm very confused by the initial step.
Explanation / Answer
a) A typical human eye will respond to wavelengths from about 390 to 700 nm. So , size of smallest object we can distinguish with light in the visible spectrum = 390 / 2 = about 195 nm
b) momentum of one electron = 9.1 * 10-31 * 7.5 × 106
= 6.825 * 10-24 kg -m/sec
c) de Broglie wavelength = h/p
= 6.63 * 10-34 / 6.825 * 10-24
= 9.714 * 10-11 m
= 0.09714 nm
d) The size of the smallest object = 0.04857 nm
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