Part A The de Broglie relation = h / p can be rewritten in terms of the wave num

Question

Part A

The de Broglie relation =h/p can be rewritten in terms of the wave number k as p=k. Recall that wave number is defined by k=2/. Using the fact that =v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2.

Express your answer as two expressions separated by a comma. Use f1, f2, v, and .

2f1v,2f2v

Part B

Find an expression for the uncertainty k=k1k2 in the wave number. Use your results from Part A.

Express your answer in terms of quantities given in Part A.

2f1v,2f2v

Explanation / Answer

We have,

k = 2 pi/lambda

lambda = v/f

k1 = 2 pi/lambda1 ; lambda1 = v/f1

k1 = 2 pi f1/v

similarly

k2 = 2 pi f2/v

Hence, k1,k2 = 2 pi f1/v, pi f2/v

B)deltaK = k1 - k2

delta k = 2 pi f1/v - 2 pi f2/v = 2 pi/v (f1 - f2)

Hence, delta k = 2 pi/v (f1 - f2) = 2 pi (f1 - f2)/v

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