An electron moves with a speed v 1.25 x 10-4c inside a one-dimensional box (V = 0) of length 48.5 nm. The potential is infi nite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?
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An electron moves with a speed v 1.25 x 10-4c inside a one-dimensional box (V = 0) of length 48.5 nm. The potential is infi nite elsewhere. The particle may not escape the box. What approximate quantum number does the electron have?
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- Chapter 38, Problem 074 Consider a potential energy barrier like that of the figure but whose height Uo is 8.6 eV and whose thickness L is 0.63 nm. What is the energy of an incident electron whose transmission coefficient is 0.0013? Energy --Ee Electron 0 L Number UnitsAn electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.45 eV. (a) What is the length L of the region? nm(b) What energy input is required to promote the electron to its first excited state? eV1) 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?
- E8A.12 At what radius does the probability density of an electron in the H atom fall to 50 per cent of its maximum value? E8A.13 At what radius in the H atom does the radial distribution function7. One electron is trapped in a one-dimensional square well potential with infinitely high sides. a. If you have a probe that has a width for electron detection Ax = 0.00350L in the x direction, for the first excited state ( n =2), what is the probability that the electron is found in the probe when it is centered at x = L/4, (hint: you can use an approximation for this - you do not need to do an integral)? b. What is the average number of electrons that you would detect using the probe described in part "b." centered at x = L/4, ifthe electron is in the first excited state (n = 2) for each experiment and you repeat the experiment N, =100,000 times?The nucleus of a typical atom is 5.0 fm (1 fm = 10-15 m) in diameter. A very simple model of the nucleus is a onedimensional box in which protons are confined. Estimate the energy of a proton in the nucleus by finding the first three allowed energies of a proton in a 5.0-fm-long box.
- A quantum system has a ground state with energy Eo = 0 meV and a 2-fold degenerate excited state with energy E₁ = 50 meV. E1 Calculate the probability of finding the system in its ground state when it is at T = 300 K. Select one: O a. 0.78 O b. 0.22 O c. 1 O d. 0.87The electron moves in an infinitely deep. potential well with a width of l=0.15 nm. a) Calculate the minimum (i.e. ground state) speed of the electron. V₁=? b) Calculate the reaction force that the electron causes when it moves back and forth and collides with the other wall of the well adiabatically (thermally insulated). F=? c) Calculate the frequency of the electron's back and forth motion. f=?