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Solve the given problem:

Problem: Let's model a nucleus as a particle trapped in the one dimensional box. Assume the particle is a proton and it is in a one-demisional nuclues of length 7.11 fm (the approximate diameter of a Pb-208 nuclues).

Part A: Determine the energies of the proton in the ground state and first two excited states. The nucleus is to absorb a photon of just the right energy to enable the proton to make an upward transition from the ground state to the second excited state.

Part B: How much energy would this be and what type of photon would it be classified as?

Please explain how you got the numbers and calculations. Thank you.

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