Elastic Collision between photon and electron

Question

A photon of wavelength !!lambda!! collides elastically with an electron at rest. The wavelength of the photon after collision becomes !!1.5 lambda!!. What is the wavelength of the electron after collision?

Solution

We can solve this question using conservation of momentum, where the momentum of both the photon and the electron can be calculated using the de Bronglie equation, i.e.,

!!p = h/λ!!

Since the electron is at rest, its initial momentum will be zero.

Therefore, the equation for conservation of momentum becomes:

!!p_("incident photon") = p_("electron") + p_("outgoing photon")!!

Therefore,

!! h/λ = (2h)/(3λ) + h/(λ_("electron"))!!

Therefore,

!!λ_("electron") = 3λ!!

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