Quantum Physics Probability Questions

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0 words  Question 2 Consider the following kaon-plus decay, 6 pts . Show that the decay is allowed by considering the various conservation rules. State any conditions on the decay. Draw a Feynman diagram for the decay. Be sure to label the hadrons, quarks and leptons, and gauge bosons. Label each particle so that the decay has a consistent color scheme. Upload Choose a File Question 3 What is the maximum energy of the electron emitted in the in MeV units. Upload Choose a File 6 pts decay of ? Give your answer Question 4 6 pts A semiconductor has a band gap of 0.85 eV. If the semiconductor is initially at room temperature, what temperature change would increase the conductivity by 50%? Upload Choose a File Question 5 Show that the kinetic energy operator eigenstates. Upload 6 pts and linear momentum operator share the same Choose a File Question 6 6 pts The work needed to pull quarks apart is so large that hadrons are created in the process. As such, quarks cannot be observed in isolation. This inability to isolate quarks is called color confinement. The mass of the lightest hadron, the meson, is 135 MeV/c2. Estimate the magnitude of the strong force within a nucleon, which is ~1 fm in size. Express your answer in newtons. Show all unit conversions. Upload Choose a File Question 7 6 pts Spectroscopic notation for an electronic configuration is 2S+1LJ, where S is the total spin quantum number, L is the total orbital angular momentum quantum number, and J is the quantum number for the angular momentum . The convention is to use letters S, P, D, etc. for L = 0, 1, 2, etc. What spectroscopic states are possible for excited-state helium having electrons in the 1s and 2p electronic states? Show how the allowed values for S, L, and J are worked out. Upload Choose a File Question 8 22 pts The Fermi gas model. The asymmetry term in the semi-empirical mass formula (Equation 9.12) describes how the binding energy is reduced (i.e., the energy of the nucleus is increased) as a nucleus moves away from the N = Z condition. In deriving the asymmetry term, we ignore electrostatic repulsion and assume the neutrons and protons are each low-temperature Fermi gases. The move away from N = Z is visualized as the shifting of neutrons over to the proton column (or vice versa) in Figure 9.7 or in the figure shown. Due to the exclusion principle, this leads to an increase in the total energy of the system. This “shifting” is at the heart of the derivation shown in Section 9.2 of the text, although the steps there are somewhat involved. Here, you will go through a simplified derivation of the asymmetry term. As always, be sure your reasoning is clear for each section of the problem. a) Assume energy levels in the nucleus are equally spaced, separated by an amount . If N0 = Z0 (i.e., N = Z initially) and neutrons are “shifted” over to become protons, show that the increase in total energy of the nucleus is . (Hint: it may be easier to consider only even .) b) Express in terms of the new N and Z of the asymmetric (N ≠ Z) nucleus. c) Assume , where is the atomic mass number. Show that this, combined with the results of parts a) and b), leads to the asymmetry term in Equation 9.12. d) Finally, justify the assumption used in c). To do this, show that to a good approximation, the Fermi energy for neutrons and the Fermi energy for protons are equal AND have the same value for all nuclei. If energy levels in the nucleus are equally spaced, show that . Upload Choose a File Question 9 17 pts Probability of electron capture. Because the nucleus is finite in size, there is a non-zero probability of finding the electron in the nucleus. In fact, electron capture is an important nuclear process. For this problem, do not use an integral table; show all steps in the integration. Cancellation of terms in any expansion must be clear. As always, reasoning must be clear. a) Show that for an electron in the ground state of hydrogen, the probability of being found in the nucleus is , where , is the radius of the nucleus, and is the Bohr radius. The hydrogen atom wave functions are found in Chapter 6. b) Use a series expansion to show that for , the probability density (probability of capture per volume) is constant. That is, show that for a small nucleus, the probability of electron capture doubles when the volume of the nucleus doubles. The following is helpful. Upload Choose a File Quiz saved at 1:24am Submit Quiz
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