Calculate the probability of exciting an electron in a one-dimensional box (actually a nanoscale wire) to...
Consider an electron in a one-dimensional box as a model of a quantum dot. Suppose the box has width 0.7 nm. For this problem, absorption of light and subsequent relaxation connect two states (i andj) with a difference in energy, AEi E - E. (a) Calculate AEsi and AE2I for luminescence from excited energy levels to the ground state. Convert the energies to the corresponding wavelengths of light, λ31 and λ21. (b) Find the wavelength of light that corresponds to...
An electron (mass m) is trapped ina 2-dimensional infinite square box of sides Lx - L - L. Take Eo = 92/8mL2. Consider the first four energy levels: the ground state and the first three excited states. 1) Calculate the ground-state energy in terms of Ep. (That is, the ground-state energy is what multiple of Eo? Eo Submit 2) In terms of Eo, what is the energy of the first excited state? (That is, the energy of the first excited...
7. We have an electron trapped in a one dimensional box, and is excited to the 2nd (n = 2) state. What will be the length of the box if our electron has the same energy as a violet photon (404 nm)?
An electron in a 10.1-nm one-dimensional box is excited from the ground state into a higher-energy state by absorbing a photon of electromagnetic radiation with a wavelength of 13,950 nm. Determine the final energy state for this transition. 04 0 0 w Na Un 0 0 1 pts Question 24
An electron is confined in the ground state in a one-dimensional box of width 10-10 m. Its energy is known to be 38 eV. (a) Calculate the energy of the electron in its first and second excited states (b) Sketch the wave functions for the ground state, the first and the second excited states (c) Estimate the average force (in Newtons) exerted on the walls of the box when the electron is in the ground state. (d) Sketch the new...
2. (a) When a particle of mass 1.0 x 10-26 g in a one-dimensional box goes from the n=3 level to n=1 level, it emits a radiation with frequency 5.0 x 1014 Hz. Calculate the length of the box. (b) Suppose that an electron freely moves around inside of a three-dimensional rectangular box with dimensions of 0.4 nm (width), 0.4 nm (length), and 0.5 nm (height). Calculate the frequency of the radiation that the electron would absorb during its transition...
What is the length of a one-dimensional box if an electron requires a wavelength of 6350 nm to be excited from the n = 2 to the n = 3 energy level?
5. An electron in a one-dimensional box of width L = .75 nm decays from the n = 3 state to the ground state by emitting two photons. What are their wavelengths?
2) If we assume the π-network in decatetraene (C10H12) to serve as a one dimensional box containing eight π-electrons that can each be assumed to behave according to the particle in a box model where each level is assumed to be doubly degenerate, and if we further assume that the molecule is linear and use the values 135 and 154 pm for the C=C and C- C bonds respectively, what wavelength of light is required to induce a transition from...
Exercise 10.14 A particle is initially in its ground state in an infinite one-dimensional potential box with sides at x = 0 and x a. If the wall of the box at x-a is suddenly moved to x = 10a, calculate the probability of finding the particle in (a) the fourth excited (n = 5) state of the new box and (b) the ninth (n 10) excited state of the new box.