Particle in a One-Dimensional Box

Tutorial for Experiment: Particle in a One-Dimensional Box

EXAMPLE: Consider a particle with a mass of 1.0 • 10-27 g and energy of 0.280 • 10-12 erg in a "box" of 14 Å. Will monochromatic light of 4730 Å excite the particle to a higher energy level?

EXPERIMENT: Radiate a particle (m = 1.0 • 10-27 g and E1 = 0.280 • 10-12 erg) in a one-dimensional box (14 Å) with monochromatic light of 4730 Å.

PROCEDURE:

  1. Select 1.0 • 10-27 g from the pull-down menu labeled "Mass."



  2. Select 14 Å from the pull-down menu labeled "Width of Box."



  3. Click the "Start" button to initiate the animation. The particle is in the ground state, the state of lowest energy E1. Observe the speed of the particle and the plot of y1 versus x. This plot is superimposed on the E1 energy level.





  4. Select 4730 Å from the pull-down menu labeled "Wavelength."




  5. And click the left button on the mouse.





RESULTS and OBSERVATIONS: After illumination the energy and speed of the particle increase. The particle is promoted to the excited state E4 as indicated by the appearance of the plot of y4 on the energy level with n = 4. The energy of the photon





is exactly equal to the difference between the allowed energies E4 and E1for the particle.



Hence, light of 4730 Å is absorbed and the particle is excited to the higher energy level E4 .