As a harmonic oscillator undergoes a transition from the ground state to the first excited state, it absorbs a photon of wavelength = 5.83 micrometers. Determine the ground state energy of the harmonic oscillator in electron volts..
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- An electron in a box is in the ground state with energy 2.0 eV. (a) Find the width of the box. (b) How much energy is needed to excite the electron to its first excited state? (c) If the electron makes a transition from an excited state to the ground state with the simultaneous emission of 30.0-eV photon, find the quantum number of the excited state?A harmonic oscillator absorbs a photon of wavelength 6.35 mm when it undergoes a transition from the ground state to the first excited state. What is the ground-state energy, in electron volts, of the oscillator?An electron is trapped in a is absorbed, the electron is in the n = 6 energy level. What was the wavelength of the absorbed photon? one-dimensional box that is 501 nm wide. Initially, it is in the n = 3 energy level but, after a photon wavelength: Eventually, the electron ends up in the ground state. As it does so, one or more photons are emitted during those transitions. Find the wavelengths of the least energetic and most energetic photons that might be emitted during all the possible transitions to the ground state. wavelength of least energetic photon: m wavelength of most energetic photon: m m
- A sodium atom in one of the states labeled “Lowest excited levels” in Fig. remains in that state, on average, for 1.6 * 10-8 s before it makes a transition to the ground state, emitting a photon with wavelength 589.0 nm and energy 2.105 eV. What is the uncertainty in energy of that excited state? What is the wavelength spread of the corresponding spectral line?6. An electron in hydrogen atom is in initial state Þ(r, 0) = A(2410o + iÞ210 + 421–1 – 2ib211) where wnim are the eigenfunctions of the hydrogen atom a. Determine the constant A b. What is the probability of finding the electron in the first excited state? hw = - n2 c. Write the state Þ(r, t) at time t, using energy eigenvalues as En d. Find the expectation value of L in the state Þ(r,t e. Find the expectation values of Lx and Ly in the state (r, t f. If measurement of Lz led to the value –ħ what will be results of measurement of energy and the square of total orbital momentum immediately afterwards and what are their probabilities?The ground-state energy of a harmonic oscillator is 5.60 eV. If the oscillator undergoes a transition from its n = 3 to n = 2 level by emitting a photon, what is the wavelength of the photon?
- Solve the following problem: Use rest mass energy of the electron 0.5 MeV Consider an atomic level with quantum numbers n = 2,l = 1 and maximum total angular momentum. a. Find the first order relativistic correction to this level, in electron- volts. b. Find the first order spin-orbit correction to this level, in electron-volts. C. Use your result in parts a and b to find the energy of that level.a. Conceptually, discuss the particle-wave duality of light. Discuss the implications of this in combination with the de Broglie (pronounced “de Broy”) equation. b. The electron of a hydrogen atom is usually no further than 1.0 Å from the proton. We can therefore say the upper limit of the radius of an isolated hydrogen atom is roughly 1.0 Å. How does the de Broglie wavelength of the electron compare to this radius? (The velocity of an electron in the first principal energy level is about 2.2 x 106 m/s). Explain why wave-particle duality is so important for quantum mechanics, yet not required in macroscopic systems that are well described by classical mechanics. c. Comment as to whether neutrons with velocity 4.14 x 103 m/s may be used to determine structures of molecules in a diffraction-based experiment. You may consider the relevant distance between atoms in molecules to be on the order of 1 Å.a. The kinetic energy of an electron is (Z + 1.5)keV. Find the de Broglie wavelength and momentum of the electron. A photon of wavelength (Z + 22) × 10¬12 m is collided with an electron from a carbon block and the scattered photon is detected at (Z + 75)' to the incident beam. Find the energy absorbed by b. the recoil electron. . Discuss (in your own words) why the Saturation Current is directly proportional to the Intensity of incident radiation in the Photoelectric Effect.
- An electron is trapped in a one-dimensional box that is 501 nm wide. Initially, it is in the n = 3 energy level but, after a photon is absorbed, the electron is in the n = 6 energy level. What was the wavelength of the absorbed photon? wavelength: .0306 Eventually, the electron ends up in the ground state. As it does so, one or more photons are emitted during those transitions. Find the wavelengths of the least energetic and most energetic photons that might be emitted during all the possible transitions to the ground state. wavelength of least energetic photon: wavelength of most energetic photon: .0753 Incorrect .0709 m Incorrect m EProblem 4: a. For Compton scattering, what photon scattering angle provides the maximum possible kinetic energy to the electron? (Please explain your answer. Hint: What angle 6 makes the wavelength difference as large as possible?) b. In this case where the electron gains the maximum kinetic energy, if the wavelength of the incident photon was 0.004960 nm, what kinetic energy did the electron gain?What electron transition in a hydrogen atom, starting from the orbit 9, will produce light of wavelength 1820 nm? What will be the corresponding energy change for the transition?