Particle in a box: A one-dimensional finite potential well has potential energy U₀= 0 in the region 0

Question

Particle in a box: A one-dimensional finite potential well has potential energy U₀= 0 in the region 0 < x < 0.2 nm, and U₀= 15 eV everywhere else. A particle with which of the energies listed below would be localized (trapped) within the potential well? (Select all correct answers.) A) 5 eV B) 20 eV C) 16 eV D) 7 eV E) None of the above.

Quizplus · Accepted Answer

For a particle to be localized within a potential well, its energy must be less than the potential energy outside the well (otherwise it would escape) but greater than the potential energy inside the well (otherwise it would tunnel through the barrier). 
In this case, the potential energy inside the well is 0 eV and the potential energy outside the well is 15 eV. Therefore, the particle's energy must be between 0 and 15 eV.
Option A (5 eV) and Option D (7 eV) both fall within this range and hence, a particle with either of these energies would be localized within the potential well. 
Options B (20 eV) and C (16 eV) have energies greater than the potential energy outside the well and hence, the particle would not be trapped within the potential well. 
Therefore, the correct answer is choice A and D.

Particle in a Box: a One-Dimensional Finite Potential Well Has