College Physics 10th Edition by Raymond Serway,Chris Vuille

Exercise 23

Using the concept of standing waves, de Broglie was able to derive Bohr's stationary orbit postulate. He assumed a confined electron could exist only in states where its de Broglie waves form standing-wave patterns, as in Figure 28.6. Consider a particle confined in a box of length L to be equivalent to a string of length L and fixed at both ends. Apply de Broglie's concept to show that (a) the linear momentum of this particle is quantized with p = mv = nh /2 L and (b) the allowed states correspond to particle energies of E n = n 2 E 0 , where E 0 = h 2 /(8 mL 2 ).