Problem: The de Broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. Recall that wave number is defined by k=2π/λ.(a) Using the fact that λ=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 π.(b) Find an expression for the uncertainty Δk=k1−k2 in the wave number. Use your results from Part (a). Express your answer in terms of quantities given in Part (a).

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(a) 

The wavenumber, k = 2π/λ

Wavelength, λ = v/f

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Problem Details

The de Broglie relation λ=h/p can be rewritten in terms of the wave number k as p=kℏ. Recall that wave number is defined by k=2π/λ.
(a) Using the fact that λ=v/f, find the wave numbers k1 and kcorresponding to frequencies f1 and f2. Express your answer as two expressions separated by a comma. Use f1, f2, v, and π.
(b) Find an expression for the uncertainty Δk=k1k2 in the wave number. Use your results from Part (a). Express your answer in terms of quantities given in Part (a).

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