Model a hydrogen atom as a three-dimensional potential well with U₀= 0 in the region ,and 0

Question

Model a hydrogen atom as a three-dimensional potential well with U₀= 0 in the region ,and 0 < z < L,and infinite otherwise,with L = 1.0 × 10^-10 m.Which of the following is NOT one of the lowest three energy levels of an electron in this model? A) 113 eV B) 226 eV C) 283 eV D) 339 eV

Quizplus · Accepted Answer

The energy levels of an electron in a hydrogen atom are given by the equation: 
En = -13.6 eV/n^2 
where n is the principal quantum number. 
In the potential well model given in the question, the electron is confined to a three-dimensional box with a length of L in the z direction and infinite in all other directions. The energy levels of such a box are given by: 
Enx,y,z = (h^2/8mL^2) (nx^2 + ny^2 + (nz/L)^2) 
where nx, ny, and nz are integers representing the number of nodes in the x, y, and z directions, respectively. 
The lowest three energy levels of this model are: 
E1 = h^2/8mL^2 = 10.2 eV 
E2 = 3h^2/8mL^2 = 40.7 eV 
E3 = 5h^2/8mL^2 = 91.4 eV 
Therefore, the answer is C, since 283 eV is not one of the lowest three energy levels of an electron in this model.

Model a Hydrogen Atom as a Three-Dimensional Potential Well with U0

Model a Hydrogen Atom as a Three-Dimensional Potential Well with U₀