Posted: December 30th, 2021
4 Photon MomentumA particle of mass m moves though a viscous medium. (See figure.) In this medium, if the particlemoves with a velocity v, it experiences a drag force Fa given by Fa = -mv/T. T is known as therelaxation time. If a particle moves through this medium without an external driving force, itsvelocity will decay exponentially to zero with a characteristic time 7 according to v(t) = v(t)e-t/T.Essentially, the particle “forgets” what it had been doing more that a few relaxation times in thepast.(F=mv/tau)- – – – – – – – -mlambdaIn this problem, the particle is illuminated from the left and absorbs photons of wavelength A atan average rate of I photons per unit time. As a result, the particle experiences an average forceand is driven to the right at an average velocity < v >. Because the photons arrive randomly asdiscrete packets, the velocity of the particle is not steady and fluctuates about the average withfluctuations of typical size Av. Your task is to compute < v > and Av.4.1 a)What is the average force experienced by the particle as a result of absorbing the photons?4.2 b)Find the average speed of the particle after a long time < v > from the condition that the totalaverage force on the particle is zero.4.3Your answer to b) should involve a factor IT. At any instant, this factor represents the total numberof photons received by the particle during the preceding relaxation time 7. Because the photonsarrive randomly, this number fluctuates. What is the size of these fluctuations? If everything elsein your expression for < v > is constant except for these fluctuations, what is Av, the size of thefluctuations in the particle’s velocity?
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