The highest achievable resolving power of a microscope is limited only by the wa
ID: 2076191 • Letter: T
Question
The highest achievable resolving power of a microscope is limited only by the wavelength used; that is, the smallest item that can be distinguished has dimensions about equal to the wavelength. Suppose one wishes to "see" inside an atom. Assuming the atom to have a diameter of 100 pm, this means that one must be able to resolve a width of, say, 10 pm. (a) If an electron microscope is used, what minimum electron energy is required? (b) If a light microscope is used, what minimum photon energy is required? (c) Which microscope seems more practical? Why?Explanation / Answer
1. for a particle in motion wavelength() and energy(E) are related as
= h/ (2*m*E)
where h = Plank'sconstant = 6.626 *10-34 J-s
m = mass = 9.1* 10-31 kg (for electron)
= 10pm = 10 *10-12
thus 10* 10-12 = 6.626 *10-34 / ( 2 * 9.1 * 10-31 *E)
Square both sides
10-22 = 4.39* 10-67 / (18.2 * 10-31 * E)
E = 2.41* 10-37 / 10-22
= 2.41*10-15 J = 2.41* 10-15 / 1.6 * 10-16 keV
As 1keV = 1.6 *10-16 J
E = 15.06 keV
2. For a photon
E = h*c/
= 6.626* 10-34 * 3 * 108 / (10* 10-12)
= 1.987* 10-14 J = 1.987 * 10-14 /(1.6 * 10-16) keV
E = 1.24* 102 keV
The electron microscope, since it needs less energy
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