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The particle in a box model is often used to make rough estimates of energy level spacings. Suppose that you have a proton confined to a one-dimensional box of length equal to a nuclear diameter (about 10−14 m).

(a) What is the energy difference between the first excited state and the ground state of this proton in the box?

(b) If this energy is emitted as a photon as the excited proton falls back to the ground state, what is the wavelength and frequency of the electromagnetic wave emitted? In what part of the spectrum does it lie?

(c) Sketch the wave function ψ as a function of position for the proton in this box for the ground state and each of the first three excited states.

(a) What is the energy difference between the first excited state and the ground state of this proton in the box?

(b) If this energy is emitted as a photon as the excited proton falls back to the ground state, what is the wavelength and frequency of the electromagnetic wave emitted? In what part of the spectrum does it lie?

(c) Sketch the wave function ψ as a function of position for the proton in this box for the ground state and each of the first three excited states.

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