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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. Using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2.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. Using the fact that λ=v/f, find the wave numbers k1 and k2 corresponding to frequencies f1 and f2.

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Answer:

[tex]k_1=\frac{2\pi f_1}{v}[/tex]

[tex]k_2=\frac{2\pi f_2}{v}[/tex]

Explanation:

v = Velocity of wave

Wavelength is given by

[tex]\lambda=\frac{v}{f}[/tex]

Wave number is given by

[tex]k=\frac{2\pi}{\lambda}[/tex]

[tex]k_1=\frac{2\pi}{\frac{v}{f_1}}\\\Rightarrow k_1=\frac{2\pi f_1}{v}[/tex]

The wave number [tex]k_1=\frac{2\pi f_1}{v}[/tex]

[tex]k_2=\frac{2\pi}{\frac{v}{f_2}}\\\Rightarrow k_2=\frac{2\pi f_2}{v}[/tex]

The wave number [tex]k_2=\frac{2\pi f_2}{v}[/tex]