The wavelength of matter as a general rule, quantum mechanics is relevant to a particle if its de broglie wavelength is of the same scale (or larger) than the characteristic size of the system, just as the wave nature of light is not relevant unless it encounters obastacles like narrow slits whose sizes are near (or smaller than) the light's wavelength. calculate the de broglie wavelength for the following cases in order to get a sense of scale. it is a good habit to learn to save time by making reasonable approximations, so i want you to use relativistic formulas only when appropriate (when it is not the case that ke mc2) and to neglect the mass energy when appropriate (when ke mc2). work with energies in ev or mev and lengths in nm or fm in order to make use of the relation hc 1240 ev-nm = 1240 mev-fm. report wavelengths in nm, a, or fm, as appropriate (a) an electron with a kinetic energy of 10 ev (a typical atomic binding energy), and compare to the size of an atom (b) an electron with a kinetic energy of 10 gev (a typical energy of an electron produced in lhc collisions), and compare to the size of a nucleus (c) a barely perceptible 0.1 g speck of dust in stil air, falling at a barely perceptible 10-4 m/s (d) use your previous result to argue whether or not a speck of dust is too massive to exhibit wave- like behavior when sent through slits of width 5 um (the smallest commercially available). hint visible light ( 500 nm) does not exhibit wave-like behavior when sent through a 'slit the size of a window (say, of width 1 m), so compare the number of wavelengths of visible light that fit inside the window, to the number of wavelengths of the dust speck that fit inside the slit. note that if a barely moving speck of dust does not exhibit detectable wave-like behavior, then certaintly anything larger (such as a person walking through a doorway) will not either. make sure that you understand this