Using the concept of standing waves, de Broglie was able

Chapter 28, Problem 28.51

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Using the concept of standing waves, de Broglie was able to derive Bohrs stationary orbit postulate. He assumed a confi ned electron could exist only in states where its de Broglie waves form standing-wave patterns, as in Figure 28.6. Consider a particle confi ned in a box of length L to be equivalent to a string of length L and fi xed at both ends. Apply de Broglies concept to show that (a) the linear momentum of this particle is quantized with p _ mv _ nh/2L and (b) the allowed states correspond to particle energies of En _ n2E0, where E0 _ h2/(8mL2).