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.

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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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.
Transcribed Image Text: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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