Question

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.

Answer 1

`k_1=(2\pi f_1)/(v)`

`k_2=(2\pi f_2)/(v)`

Step-by-step explanation:

v = Velocity of wave

Wavelength is given by

`\lambda=(v)/(f)`

Wave number is given by

`k=(2\pi)/(\lambda)`

`k_1=(2\pi)/((v)/(f_1))\\\Rightarrow k_1=(2\pi f_1)/(v)`

The wave number
`k_1=(2\pi f_1)/(v)`

`k_2=(2\pi)/((v)/(f_2))\\\Rightarrow k_2=(2\pi f_2)/(v)`

The wave number
`k_2=(2\pi f_2)/(v)`