The moon has a mass of 7.35 * 1022 kg, and the length of a sidereal day is 27.3 days. (a) Estimate the de Broglie wavelength of the moon in its orbit around the earth. (b) Using Mearth for the mass of the earth and Mmoon for the mass of the moon, we can use Newton’s law of gravitation to determine the radius of the moon’s orbit in terms of an integer-valued quantum number m as Rm = m2amoon, where amoon is the analog of the Bohr radius for the earth–moon gravitational system. Determine amoon in terms of Newton’s constant G, Planck’s constant h, and the masses Mearth and Mmoon. (c) The mass of the earth is Mearth = 5.97 * 1024 kg. Estimate the numerical value of amoon. (d) The radius of the moon’s orbit is 3.84 * 108 m. Estimate the moon’s quantum number m. (e) The quantized energy levels of the moon are given by E = -E0/m2. Estimate the quantum ground-state energy E0 of the moon.
The moon has a mass of 7.35 * 1022 kg, and the length of a sidereal day is 27.3 days. (a) Estimate the de Broglie wavelength of the moon in its orbit around the earth. (b) Using Mearth for the mass of the earth and Mmoon for the mass of the moon, we can use Newton’s law of gravitation to determine the radius of the moon’s orbit in terms of an integer-valued quantum number m as Rm = m2amoon, where amoon is the analog of the Bohr radius for the earth–moon gravitational system. Determine amoon in terms of Newton’s constant G, Planck’s constant h, and the masses Mearth and Mmoon. (c) The mass of the earth is Mearth = 5.97 * 1024 kg. Estimate the numerical value of amoon. (d) The radius of the moon’s orbit is 3.84 * 108 m. Estimate the moon’s quantum number m. (e) The quantized energy levels of the moon are given by E = -E0/m2. Estimate the quantum ground-state energy E0 of the moon.
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