Consider making an artificial atom that mimics hydrogen by placing an electron in a one-dimensional infinitely deep potential well (instead of the Coulomb potential produced by a proton in a real hydrogen atom).What well width is required to produce an energy separation between the ground state and first excited state in the well that is the same as in hydrogen (E_{1st excited} - E_ground= 10.2 eV)? A)0.1 nm B)0.3 nm C)0.5 nm D)2 nm E)5 nm

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Quizplus · Accepted Answer

In hydrogen atom, the energy separation between ground state and first excited state is 10.2 eV. For a one-dimensional infinitely deep potential well, the energy separation between the ground state and first excited state can be calculated as: E_{- E} = (h^2/8mL^2) * (pi)^2 where h is the Planck's constant, m is the mass of the electron, and L is the width of the well. Equating this to the energy separation in hydrogen, we get: (h^2/8mL^2) * (pi)^2 = 10.2 eV Solving for L, we get: L = sqrt(h^2/8m * (pi)^2 / 10.2) = 0.307 nm Therefore, the best choice is B (0.3 nm).

Consider Making an Artificial Atom That Mimics Hydrogen by Placing