Analysis of a reaction mixture finds the following: [CO] = 1…

Analysis of a reaction mixture finds the following: [CO] = 1.48 x 10-6 M [Cl2] = 9.50 x 10-7 M [COCl2] = 0.0100 M a) calculate Q (show your work on scratch paper). b) in the blank, indicate if the reaction is moving forward, reverse, or at equilibrium. Show your work for “a,” and upload a photo or scan to Quiz 4 in Assignments.

Question 1: 20 points 1. An electron is at rest at the origi…

Question 1: 20 points 1. An electron is at rest at the origin, in the presence of a magnetic field whose magnitude (B0) is constant but whose direction rides around at constant angular velocity ω on the lip of a cone of opening angle α: B(t) = B0[sin(α) cos(ωt)ˆi + sin(α) sin(ωt)ˆj + cos (α)ˆk]                                                         (1) 1a) Write the formula for the Hamiltonian for a particle with spin coupled to a magnetic field. (You only need to write the coupling Hamiltonian.)[5 points] 1b) Construct the 2 × 2 Hamiltonian matrix for this system. [5 points] 1c) Use first-order time-dependent perturbation theory to calculate the approximate probability of a transition from spin up (the initial state) to spin down, as a function of time. [5 points] 1d) State the criterion on the strength of the field that determines whetherperturbation theory is applicable in this case. [5 points]  

Question 4 – 15 points 4. Some radioactive nuclei, e.g. Phos…

Question 4 – 15 points 4. Some radioactive nuclei, e.g. Phosphorus-32, emit electrons (“beta radioactivity”). Here we consider if Gamow’s model of radioactivity can be applied to understand beta emission. 4a) As in the case of alpha emission, consider the electron to be trapped inside the original nucleus in a square well. Outside the square well, the electron will feel the Coulomb force due to the final nucleus. Write an expression for the energy of the electron as a function of the distance from the nucleus. [5 points] 4b) Sketch the potential of part a). [5 points]   4c) Discuss if Gamow’s model can be applied to beta decay. [5 points]