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Atomic Energy Levels and Wave-Particle Duality Quiz 20 points E = 20 points Objective 13.B.1: Explain wave-particle duality of the atom and how it relates to the concept of de Broglie wavelength. Objective 13.B.3: Draw a diagram to depict the energy levels of an atom and analyze the energy and wavelength of a photon emitted or absorbed in a transition between energy levels. 1. Energy-level diagrams for atoms that comprise a helium-neon laser are given above. As indicated on the let, the helium atom is excited by an electrical discharge and an electron jumps from energy level E0 to energy level E2. The helium atom (atomic mass 4) then collides inelastically with a neon atom (atom mass 20), and the helium atoms falls to the ground state, giving the neon ' ' atom enough energy to raise an electron from E0 to E 2 . The laser emits light when an electron ' ' in the neon atom falls from energy level E 2 to E1 . (a) Calculate the minimum speed the helium atom must have in order to raise the neon electron ' ' from E0 to E 2 . (b) Calculate the de Broglie wavelength of the helium atom when it has the speed determined in (a). ' ' (c) The excited neon electron then falls from E 2 to E1 and emits a photon of laser light. Calculate the wavelength of this light. (d) The laser light is now used to repair a detached retina in a patient’s eye. The laser puts out 3 pulses of length 20 10 s that average 0.50 W output per pulse. How many photons does each pulse contain? a. (a) 4 points Energy is conserved: 1 1 1 mHe v0 mHe v12 mNev0 (E2 E2 ) , where v0 is the minimum speed of the helium atom 2 2 ' 2 2 2 before the collision, and v1 and v2 are the speeds of the helium and neon atoms after the collision respectively. Any one of the following assumptions is correct for v1 and v2: a. v1 = 0 and v2 = 0 b. v1 = 0 and v2 not = 0 c. v1 not = 0, v2 not = 0, and v1 not = v2 d. v1 not = 0, v2 not = 0, and v1 = v2 Momentum is conserved: mHe v0 mHe v1 mNe v2 Any one of the following assumptions is correct for v1 and v2: e. v1 = 0 and v2 not = 0 f. v1 not = 0, v2 not = 0, and v1 not = v2 g. v1 not = 0, v2 not = 0, and v1 = v2 The final answer depends on the assumption used in the equations. (b) 4 points (there is an alternate solution to arrive at same answer) h h de Broglie wavelength: λ p mv Use the answer from (a) to substitute and find correct answer. (c) 6 points E 20.66 eV 18.70 eV f 4.73 1014 Hz h 4.14 1015 eV s c 3.0 108 m/s λ 634 nm f 4.73 1014 Hz (d) 6 points E Pt E (0.50 W)(20 103 s) E 1 102 J 6.25 1016 eV E 6.25 1016 eV N 3.19 1016 photons E2 E1 (20.66 eV 18.70 eV) ' '