8) Particle Standing Waves Since electrons and other particles can act as waves, it is unsurprising that they can also form standing wave patterns similar to those we saw by shaking the rubber tubing last activity. Imagine that we placed some particle of mass m inside a small box. Since, as we saw in part A, the "wave" nature of a particle is associated with the probability of nding it at a particular location, we expect that the wave should go to zero at the walls of the box. That is, we expect the walls of the box to act like nodes for our particle wave. 1) Based on this, draw pictures of the rst few particle standing waves that can be placed in a 1D box of length L. What is the pattern for possible particle wavelengths, A, that may fit in this box? 2) Using the de Broglie relation and your answer to question 1, nd an equation for the possible momenta, p, that the particle may have. 3) In 7A you learned that the kinetic energy of a particle could be written as KE = 1 mV2 , and in 7B you 2 learned that the momentum of a particle is p 2 H111. Using these relationships rewrite KE in terms of p and use your results from 2 to nd the possible kinetic energies the particle may have. What happens to the energy as the wavelength of the particle decreases