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Chapter 7: Q68E (page 283)
Roughly, how does the size of a triply ionized beryllium ion compare with hydrogen?
The Triple ionized beryllium ion is roughly as compared to the radius of the hydrogen atom.
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Question: Consider a cubic 3D infinite well of side length of L. There are 15 identical particles of mass m in the well, but for whatever reason, no more than two particles can have the same wave function. (a) What is the lowest possible total energy? (b) In this minimum total energy state, at what point(s) would the highest energy particle most likely be found? (Knowing no more than its energy, the highest energy particle might be in any of multiple wave functions open to it and with equal probability.)
Question: Show that the angular normalization constant in Table 7.3 for the case is correct.
Consider a vibrating molecule that behaves as a simple harmonic oscillator of mass , spring constant 103N/m and charge is +e , (a) Estimate the transition time from the first excited state to the ground state, assuming that it decays by electric dipole radiation. (b) What is the wavelength of the photon emitted?
A comet of mass describes a very elliptical orbit about a star of mass , with its minimum orbit radius, known as perihelion, being role="math" localid="1660116418480" and its maximum, or aphelion, times as far. When at these minimum and maximum
radii, its radius is, of course, not changing, so its radial kinetic energy is , and its kinetic energy is entirely rotational. From classical mechanics, rotational energy is given by , where is the moment of inertia, which for a “point comet” is simply .
(a) The comet’s speed at perihelion is . Calculate its angular momentum.
(b) Verify that the sum of the gravitational potential energy and rotational energy are equal at perihelion and aphelion. (Remember: Angular momentum is conserved.)
(c) Calculate the sum of the gravitational potential energy and rotational energy when the orbit radius is times perihelion. How do you reconcile your answer with energy conservation?
(d) If the comet had the same total energy but described a circular orbit, at what radius would it orbit, and how would its angular momentum compare with the value of part (a)?
(e) Relate your observations to the division of kinetic energy in hydrogen electron orbits of the same but different .
A hydrogen atom in an n = 2 state absorbs a photon,
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