In the previous activity we considered electrons which entered in a TV screen and had enough energy to go on through. However, the probability interpretation indicates that not all electrons just keep going. If they did, the probability on each side of the boundary would be identical. Some of the electrons bounce back, but most go on through.
In many situations electrons arrive at a metal where they do not have sufficient energy to go through. The potential energy results from a repulsion and is larger than the total energy of the incoming electrons. Such a situation is shown in Figure 1.
For this situation, describe the motion that you would expect for the electrons.
Calculate the kinetic energy and wavelength of the electrons in empty space.
Calculate the kinetic energy of the electron inside the metal.
You have just uncovered a problem. The kinetic energy that you calculated is negative. But, only positive quantities --- mass and speed squared --- are involved in kinetic energy. It must be a positive number.