5. This question is about energy levels of a hydrogen atom. The three lowest energy levels of electrons bound to a proto

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5 This Question Is About Energy Levels Of A Hydrogen Atom The Three Lowest Energy Levels Of Electrons Bound To A Proto 1 (55.56 KiB) Viewed 35 times

5. This question is about energy levels of a hydrogen atom. The three lowest energy levels of electrons bound to a proton are given by E1 = -13.60 eV, E = -3.40 eV, E3 = -1.51 eV as illustrated by the diagram below. (a) 2 points What is the explanation of the discrete spectrum of energy states for an electron orbiting" a proton in terms of the Bohr model of atoms? (No need to do a full derivation: just state the basic assumption/condition that leads to a discrete energy spectrum starting from the de Broglie waves for electrons.] (6) 2 points What is the mathematical pattern that connects the above energy levels E, for n=1,2,3 and how is n connected to the condition you mentioned in part (a)? (c) 2 points What is the minimum frequency of electromagnetic radiation that can ionize a hydrogen atom, i.e. remove an electron from the lowest energy state (round to three significant digits)? [Hint: 1eV is approximately 1.6 x 10-19 J.] (d) 2 points for transitions between the above energy levels E1, E2, E3, photons of what three wavelengths can be emitted by the hydrogen atom (round to the nearest nanometer)? Could you see any of those wavelengths with the naked eye? (e) 2 points What is the de Broglio wavelength of a macroscopic object such as 5 g bullet moving at 340 m/s? Comment on the length scale in comparison to the size of the bullet and whether we would cver notice it?
O eV Energy 3 -1.51 eV n=2 -3.40 eV Ground state n=1 -13.60 eV