A photon with momentum 1.19*10^-24Ns moving toward the right collides with a sta

Question

A photon with momentum 1.19*10^-24Ns moving toward the right collides with a stationary electron. The photon movees off with a momentum of 7.65*10^-25Ns at an angle of 50 degree above the horizontal while the electron moves off at an angle of 40 degree below the horizontal.

a. Calculate the momentum of the electron after the collision.

b.Determine the speed of the electron after the collision.

c. after the collsion, the frequency of the photon has _____(shift higher, shift lower, not shift)

d. calculate the shift in the wavelength of the photon during the collision.

Explanation / Answer

a) Conservation of momentum,

Horizontal,   1.19*10^-24 = 7.65*10^-25*cos50 + meve*cos40

  meve = (1.19*10^-24 - 4.92*10^-25)/cos40 = 9.11*10^-25 Ns

b) speed of electron = 9.11*10^-25/9.11*10^-31 = 10^6 m/s

c) wavelength of photon before collision Li = h/pi = 5.55*10^-10 m

frequency = fi = c/Li = 3*10^8/5.55*10^-10 = 5.4*10^17 Hz   

wavelength of photon after collision Lf = h/pf = 8.63*10^-10 m

frequency = fi = c/Li = 3*10^8/8.63*10^-10 = 3.48*10^17 Hz

Thus after the collsion, the frequency of the photon has shift lower.

d)  the shift in the wavelength of the photon during the collision = Lf - Li = 3.08*10^-10 m

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