Particle in a box: The ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm is 20 eV. The ground state energy of the same particle in a one-dimensional finite potential well with U₀= 0 in the region 0

Question

Particle in a box: The ground state energy of a particle in a one-dimensional infinite potential well of width 1.5 nm is 20 eV. The ground state energy of the same particle in a one-dimensional finite potential well with U₀= 0 in the region 0 < x < 1.5 nm, and U₀= 50 eV everywhere else, would be A) less than 20 eV. B) greater than 20 eV. C) equal to 20 eV. D) The particle would not have a ground state.

Quizplus · Accepted Answer

The ground state energy of a particle in a finite potential well is always greater than or equal to the ground state energy of a particle in the corresponding infinite potential well. Since the potential outside the region 0 < x < 1.5 nm is 50 eV, the ground state energy in this finite potential well will be higher than 20 eV. Therefore, the answer is A, less than 20 eV.

Particle in a Box: the Ground State Energy of a Particle