A proton is trapped in an infinitely deep square well of width L = 5 ×...

A proton is trapped in an infinitely deep square well of width L = 5 × 10^-6 nm. This is approximately the size of an atomic nucleus. (It depends on atomic weight.) The proton's mc² = 9.3827 × 10⁸ eV. Note: Atomic nuclei are really spheres. For simplicity, we are treating them as 1-D square wells, which yields the correct order of magnitude result.

1) What is the ground state energy of the proton in this well in eV? E₁ =

2) If the proton is in an excited state, it can fall to a lower energy state and emit a photon (just like an electron does). Suppose the photon's energy is 4.0959 × 10⁷ eV.

Note: This photon is a gamma ray, common in nuclear transitions. What was the proton's initial energy level (i.e., the n value)? n =

3) Suppose an electron were trapped in this well (infinitely deep, with the same width, L). What is the electron's ground state energy in this well in eV? E₁ =

Expert Solution

genius_generous answered 6 months ago

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