18. Doubly-ionized lithium (Z = 3) undergoes a transition from the n = 2 to the n = 1 state by emission of a single photon. The photon is absorbed by a system constructed of an electron in a one-dimensional harmonic oscillator potential that is initially in its ground state. What are the two largest possible values of the characteristic frequency wo of the harmonic oscillator that absorbed the photon?
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- 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 UnitsThe Rydberg constant for a Hydrogen atom is R = 1.097 x 107 m-1. What is the ionisation energy of Hydrogen? Select one: a. 10.6 eV b. 5.7 eV c. 7.8 eV d. 13.6 eV3. 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:
- Which of these expressions would yield the wavelength of light in meters emitted when an electron drops from orbit n = 3 to n = 2 in a Bohr hydrogen atom? Given h = 4.14 x 10-15 eVs and c = 3.00 x 108 m/s. a. 1.89/hxc b. hc/1.89 c. 1.89 x h x c d. (1.51 + 3.4)/hc e. hc/3.4If the Bohr radius of the n = 3 state of a hydrogen atom is R, then the radius of the ground state is A. 9R. B. 3R. C.R/3. D. R/9. Answer is D, please explain and write clearly.An electron is excited from the n=1 ground state to the n=3 state in a hydrogen atom. Which of the following statements are true? Correct the false statements to make them true. (It may help to draw the Bohr model of the atom with the corresponding electron orbits.)a. It takes more energy to ionize (completely remove) the electron from n = 3 than from the ground state.b. The electron is farther from the nucleus on average in the n = 3 state than in the n = 1 state.c. The wavelength of light emitted if the electron drops from n = 3 to n = 2 will be shorter than the wavelength of light emitted if the electron falls from n = 3 to n = 1.d. The wavelength of light emitted when the electron returns to the ground state from n = 3 will be the same as the wavelength of light absorbed to go from n = 1 to n = 3.e. For n = 3, the electron is in the first excited state.
- 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.An electron is in the n = 4 orbit of an hydrogen atom. It returns to the ground state with emission of light. The Rydberg constant is R = 1.097 x 107 m-1. What is the frequency of the light emitted? Select one: a. 2.74 x 1014 Hz b. 8.23 x 106 Hz c. 3.08 x 1015 Hz d. 10.28 x 106 Hz