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Chapter 34: Problem 12
If you measure a particle's position with perfect accuracy, what do you know about its momentum?
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Show that Wien's law (Equation \(34.2 \mathrm{a}\) ) follows from Planck's law (Equation 34.3 ). (Hint: Differentiate Planck's law with respect to wavelength.)
You're a cell biologist who wants to image micro tubules that form the "skeletons" of living cells. The micro tubules are \(25 \mathrm{nm}\) in diameter, and, as Chapter 32 shows, you need to image with waves whose wavelength is at least this small. You can use either an inexpensive electron microscope that accelerates electrons to kinetic energies of \(40 \mathrm{keV},\) or a more expensive unit that produces 100-kev electrons. Will the less expensive microscope work?
Ultraviolet light with wavelength \(75 \mathrm{nm}\) shines on hydrogen at oms in their ground states, ionizing some of the atoms. What' the energy of the electrons freed in this process?
An energy uncertainty of \(1 \mathrm{MeV}\) corresponds to a particle lifetime closest to a. \(10^{-34} \mathrm{s}\) b. \(10^{-21} s\) c. \(10^{-9} \mathrm{s}\) d. \(1 \mu s\)
An experimental transistor uses a single electron trapped in a channel \(6.6 \mathrm{nm}\) wide. What's the minimum kinetic energy this electron could have, consistent with the uncertainty principle? Give your answer in joules and ineV.
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