ps4soln

# ps4soln - ELEC 262 Problem Set 4 solutions 1(a The model...

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ELEC 262 - Problem Set 4 solutions 1. (a) The model developed in lecture predicts that the metal should become transparent for frequencies equal to (and above) the plasma frequency. The plot shown in lecture illustrates an abrupt drop in the reflectivity (and therefore an increase in the transmission) at a photon energy of about 16 electron volts (eV). This is a good approximation of the photon energy corresponding to the plasma frequency. Using h = 4.13 × 10 -15 eV sec, we find that 15 3.87 10 Hz ν ==× Eh . (b) λ = 2 nm corresponds to a frequency that is well above the plasma frequency: ν = c/ λ = 1.5 × 10 17 Hz. So the refractive index is very close to (but slightly less than) one: 2 2 1 0.9997 ν =− = ν P n (c) We compute the derivative 22 ν ν = ν ν −ν P P dn d . For ν > ν P , this is always positive. Thus the material exhibits normal dispersion. 2. The power radiated by an accelerating charge is given by the Larmor formula: () 3 0 a 6c = q Pt πε In this case, the acceleration is simply given by the centripetal acceleration of a circulating electron: a = v 2 /R, where v is the velocity of the electron and R is the radius of the circle. Putting

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ps4soln - ELEC 262 Problem Set 4 solutions 1(a The model...

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