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Question: 5 20 points a proton of mass m inside a...

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5. (20 points) A proton of mass m, inside a nucleus is in a harmonic oscillator potential U(o) K nucleus. where r is the distance from the centre of the a) Write Newtons 2nd Law for this proton assuming it moves in a circular orbit, expressing the acceleration in terms of the speed v and the radius r of the circular orbit b) Virial Theorem for the harmonic oscillator: Using the equation you wrote in a), Express the kinetic energy mv in terms of the potential energy of the harmonic oscillator. c) Solve the Bohr postulate together with the equation you wrote in a), to find the radius r, of the allowed orbits for the proton inside the nucleus. d) Find the energy levels E,. Express E, in terms of the harmonic oscillator frequency
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