1 (a) Show that the entropy per photon in blackbody radiation is independent of the temperature, and in d spatial dimensions is given by - d-- 1 s = (d + 1) " E n-d n=1 %3D n=1 (b) Show that the answer would have been d + 1 if the photons obeyed Boltzman statistics.

(c) Below is the expression of quantized subband energy in a quantum well photodetector where the m* and Wz are the carrier effective mass and well width, respectively, and the rest are constants. Derive the wavelength detected based on intersubband transition. En = ħ2 nn *W. 2m Z

Find v* for N2 gas in air (a) on a cold day at T = 15°C and (b) on a hot day at T = 35°C.

What is the energy of a light quantum (photon) which has a wavelength of 600nm? Compare the energy with the electron wave energy calculated in problem 2 (6.6935 x 10-25) and disscuss the difference.

A beam of atoms moving in a certain direction can be slowed down if they absorb photons from a laser beam moving in the opposite direction and subsequently spontaneously emit photons isotropically. For a beam of Sodium atoms (mass number A = 23) with speed 600ms-1, if a laser beam of wavelength 589 nm is used, the number of such absorption and emission cycles needed to bring a Sodium atom to rest would be approximately (a) 1.3 x 105 (b) 1.3 x 104 (c) 2.1 x 103 (d) 2.1 x 104

What is the longest wavelength (in m} of the EM radiation that can eject photoelectrons from a certain metal target, given that the binding energy is 6.81 eV? Exponential format with 3 SF.

The sun can be treated as a blackbody at 5780 K. Using EES (or other) software, calculate and plot the spectral blackbody emissive power Ebl of the sun versus wavelength in the range of 0.01 µm to 1000 µm. Discuss the results.  

In an experiment done by scattering 5.5-MeV ∝ particles from a thin gold foil, students fi nd that 10,000∝ particles are scattered at an angle greater than 50°. (a) How many of these  particles will be scattered greater than 90°? (b) How many will be scattered between 70° and 80°?

The wavelength λmax at which the Planck distribution is a maximum can be found by solving dρ(λ,T)/dT = 0. Differentiate ρ(λ,T) with respect to T and show that the condition for the maximum can be expressed as xex − 5(ex − 1) = 0, where x = hc/λkT. There are no analytical solutions to this equation, but a numerical approach gives x = 4.965 as a solution. Use this result to confirm Wien’s law, that λmaxT is a constant, deduce an expression for the constant, and compare it to the value quoted in the text.

tionary free electron gains when a photon scatters from it. We can plot K versus the an- gle o at which the photon scatters; see curve 1 in Fig. 38-21. If we switch the target to be a stationary free proton, does the end point of the graph shift (a) upward as suggested by curve 2, (b) downward as suggested by curve 3, or (c) remain the same? 3. 180° Figure 38-21