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- 14. Verify that the parities of the one-electron atom eigenfunctions 300, 310, 320, and 322 are determined by (-1)¹.9. A system of 9 identical non-interacting spin-3/2 particles confined to a one-dimensional harmonic oscillator potential is in its minimum energy configuration for which E = 5.75 eV. What is the minimum energy of the same system with 10 such particles? Recall that the energy levels of a single particle in a one-dimensional harmonic oscillator potential are given by En = (n +) with n = 0, 1, 2,.... hwnFind the possible total spin angular momentum quantum number under LS coupling of two atomic electrons whose orbital numbers are l1 = 1 and l2 = 2 42,1,0 21,0 3,2,1
- Electrons in a hydrogen atom are in a 3p excitation state transitioning radiative to energy level 2s. Taking into account the spin orbital interaction, determine : i) What is a spin orbit interaction?ii) Show the separation of 3p and 2s energy levels in the energy level diagramwithout an external magnetic field Biii) Show the separation of 3p and 2s energy levels in the energy level diagram due to the presence of an external magnetic field Biv) State the allowed transition conditionsv) Energy emitted when in space without a magnetic fieldvi) Energy emitted if it is in a space with a magnetic field B = 1Tplease solve part i-7 For hydrogen atom electron, with Spin , in the state a -A(), Determine A, , of Sx, Sy,S2 13217水 and with spin State x く>,くら、?,くら,>, and3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction is (2a.)3/2 /3a. 2ao , where a, is the Bohr radius. (a) 2-axis? What possible angles might the angular momentum vector L make with the (b) What is the most probable radius (in terms of a,) at which the electron is found? (c) What is the expectation value of r in this state? Note: xe-"dx = 120. (p) S° x*e-dx = 23.91. What is the probability of finding such an electron between a, and oo? Note:A hydrogen atom is placed in a 2.4 T magnetic field. What are the possible energy values for a 2p electron with and without magnetic field if we dont consider spin?11. The Hamiltonian for an electron in a hydrogen atom subject to a constant magnetic field B is given by H = e2 p² 2me Απεργ e + (L+2S). B 2me where L and S are the angular momentum and spin operators respectivelyr. Assume the magnetic field points in the z-direction. (a) How many distinct energy levels will the n = : 3 state have? = = 3,1 = 2) → (n = 2,1 = 1). Find the energy of the (b) Consider the line corresponding to the transition (n emitted photons (hw AE, with AE = the energy difference between initial and final state), assuming the possible transitions are constrained by the selection rule Am = 0,±1.7. For the 3p and 3d states of hydrogen, show that (-) avg =1/1290. ao. n²