A proton is trapped inside a cubical "quantum box" whose sides have length L
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics
Problem
A proton is trapped inside a cubical "quantum box" whose sides have length L. The potential energy outside the box is effectively infinite, so the proton cannot escape. Initially, L is 2.0 fm (1 fm = 10^{-15} m). The box then expands slowly to a new side length of 3.0 fm while the proton remains in its quantum ground state throughout the expansion.
(a) Derive an expression for the ground-state energy of the proton as a function of L, clearly indicating all constants and quantum numbers that appear.
(b) Calculate the ratio of the proton’s final ground-state energy after expansion to its initial ground-state energy before expansion.
(c) Suppose the energy change between the two ground states were carried by a single photon. Determine the photon energy that would need to be emitted or absorbed.
(d) Based on the photon energy you found, classify the radiation (for example, radio, microwave, infrared, visible, ultraviolet, X-ray, or gamma-ray) and justify your classification.