3. With the aid of an energy level diagram, use the angular momentum selection rules to determine the possible transitions that can de-excite the following states in the H atom. (a) The 4p state. (b) The 5g state.
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Q: 4. Find the most probable radial position of an electron in the 3d state of the hydrogen atom.
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- 1. List all possible states of a hydrogen atom that have E=-1.51 eV.Chapter 39, Problem 044 A hydrogen atom in a state having a binding energy (the energy required to remove an electron) of -1.51 eV makes a transition to a state with an excitation energy (the difference between the energy of the state and that of the ground state) of 10.200 eV. (a) What is the energy of the photon emitted as a result of the transition? What are the (b) higher quantum number and (c) lower quantum number of the transition producing this emission? Use -13.60 eV as the binding energy of an electron in the ground state. (a) Number Units (b) Number Units (c) Number Units22:39 Wed 14 Dec Question 2 A hydrogen atom is in the n = 55 state. X (b) Calculate the change in energy for a transition from the n = 55 state to the n = 56 state. (c) Calculate the wavelength of the photon that is absorbed in the transition in (b). @ 4% 7
- 3. 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:3. Suppose an electron in a hydrogen atom is in a 2p state, and the radial wavefunction e 2ao, where a, is the Bohr radius. 1 is (2ао)3/2 VЗа. (а) What possible angles might the angular momentum vector L make with the Z-axis? (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: S xe-"dx 120. (d) What is the probability of finding such an electron between a, and ∞? Note: ° x*e-"dx = 23.91.4. In describing the atom, we often refer to the "electron cloud." Does this mean that the electron is spread out in space in the form of a cloud? Just what is that cloud? In hat ratio would vou expet Ma and Clto combine? ? Why?
- 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