# 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!!