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a) The de Broglie wavelength of an electron is 2.33 nm. Use the Bohr model of the hydrogen
atom to calculate the state that the electron is in.
b) Compare the de Broglie wavelength to the circumference of the orbit.

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3:42 .ull 5G Done 2 of 2 John Isner holds the ATP's (Association of Tennis Professionals) official record for the fastest serve at 253 km/h. Calculate the de Broglie wavelength of a tennis ball with the standard weight of 54.6 grams. Give your answer in 1034 m (for example, if your answer is 5.6x1034 m, then enter 5.6). This should give you a good idea of why one cannot expect to observe interference affects using tennis balls rather then, for example, electrons. +)
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c) The Bohr model of the atom postulated electrons orbiting around the nucleus in stable orbits. De Broglie explained what orbits could exist by postulating that electrons (and any- thing else) with momentum p have an associated wavelength λ, given by λ=h/p where h is Planck's constant. i) For an electron orbiting around a proton (the Bohr model), equating the centripetal force with the Coulomb force gives the expression v² = e²/(4πεmer). Calculate the speed of an electron orbiting at the Bohr radius, ˜Â = 0.053 nm. ii) Calculate the momenta and the de Broglie wavelengths of the electron of part (i) and of a bird (a racing pigeon) that weighs 0.350 kg and flies at 100 km per hour. iii) Compare the wavelength for the electron that you obtain in (ii) with the circumference of the orbit. Comment on this comparison. Explain briefly what it implies about the other possible orbits of the Bohr model and how the higher orbits might be predicted.
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