A photon moving in the +x-direction, scatters off a free stationary electron. Th

Question

A photon moving in the +x-direction, scatters off a free stationary electron. The wavelength of the incident photon is 0.0250 nm. After the collision, the electron moves at an angle below the +x-axis, while the photon moves at an angle = 83.3° above the +x-axis. (For the purpose of this exercise, assume that the electron is traveling slow enough that the non-relativistic relationship between momentum and velocity can be used.)

(a)

What is the angle (in degrees)? angle in particular is counterclockwise from the +x-axis

(b)

Determine the speed of the electron (in m/s).

Explanation / Answer

Using de broglie hypothesis we can give the momentum of the photon

p= h/lamda

p = 6.64E-34/2.5E-11 = 2.66E-23 kgms^-2

Now using conservation of linear momentum is both the directions will give the angle and electron velocity

Let the electron momentum be Pe  

P cos (83.3) + Pe   cos (alpha) =  2.66E-23 kgms^-2

P sin (83.3) +Pe sin ( alpha) = 0

Solving this we will get the answer

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