) Determine the energy of a photon emitted when an electron relaxes from the excited state ν=4 to ground state ν=1 of a harmonic oscillator if the force constant κ is 285 N m–1.
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- a) [2018] State Kirchhoff’s two Laws, and give the fundamental physical principles which each law expresses. b) De Broglie explained the Bohr model of the hydrogen atom by attributing a wavelength λ toa particle, with the value of λ coming from the momentum p = mv as λ = h/p.i) Calculate the de Broglie wavelength of a bird (a racing pigeon) that weighs 0.350 kgand flies at 100 km per hour.ii) Equating the centripetal force on an electron orbiting around a proton with the Coulomb force gives the expression v2 = e2/(4πε0mer). Calculate the speed of an electron or- biting at the Bohr radius, rB = 0.053 nm.iii) Calculate the momentum and the de Broglie wavelength of an electron moving at the speed you obtain in (ii).iv) Compare the wavelength you obtain in (iii) with the circumference of the orbit. Com- ment on this comparison. Explain briefly what it implies about the possible orbits of the Bohr model and how the higher orbits might be predicted. c) Thorium-234 is…A Quantum system has a ground state with energy E0 = 100meV and a 3-fold degenerate excited state with energy E1 = 100meV . Calculate the probability of finding the system in its groud state when it is at T = 300 K? a) 0.94 b) 0.06 c) 1 d) 0.98(15) Electrons photo-emitted from a material in a UPS experiment can be viewed as free particles. A photon of wavelength 100 nm is absorbed by an electron that was in an orbital with an ionization energy IE of 8.41 eV. Use the relationship between kinetic energy and momentum (KE = p²/2m) and the quantum mechanical momentum operator p to solve for the exact unnormalized wavefunction of the electron that is photo-emitted from the orbital. Consider the +X direction only.
- 1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?(b) Evaluate the ratio of the de Broglie wavelength of electron to that of proton when (m₂=9.11 × 10-3¹ kg, mp=1.67 × 10-27 kg) (i) both have the same kinetic energy. (ii) The electron kinetic energy is 1000 eV, and the proton kineticThe smallest atoms can themselves exhibit quantum mechanical behavior Calculate the de Broglie wavelength (in picometers) of a hydrogen atom traveling at 430 m/sm/s. Express your answer using three significant figures.