4 Photon Momentum
A particle of mass m moves though a viscous medium. (See figure.) In this medium, if the particle
moves with a velocity v, it experiences a drag force Fa given by Fa = -mv/T. T is known as the
relaxation time. If a particle moves through this medium without an external driving force, its
velocity will decay exponentially to zero with a characteristic time 7 according to v(t) = v(t)e-t/T.
Essentially, the particle quot;forgetsquot; what it had been doing more that a few relaxation times in the
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In this problem, the particle is illuminated from the left and absorbs photons of wavelength A at
an average rate of I photons per unit time. As a result, the particle experiences an average force
and is driven to the right at an average velocity lt; v gt;. Because the photons arrive randomly as
discrete packets, the velocity of the particle is not steady and fluctuates about the average with
fluctuations of typical size Av. Your task is to compute lt; v gt; and Av.
What is the average force experienced by the particle as a result of absorbing the photons?
Find the average speed of the particle after a long time lt; v gt; from the condition that the total
average force on the particle is zero.
Your answer to b) should involve a factor IT. At any instant, this factor represents the total number
of photons received by the particle during the preceding relaxation time 7. Because the photons
arrive randomly, this number fluctuates. What is the size of these fluctuations? If everything else
in your expression for lt; v gt; is constant except for these fluctuations, what is Av, the size of the
fluctuations in the particle’s velocity?Science