Use the thermodynamic identity dU = TdS - PdV to show that the energy density of a photon gas is proportional to T4.
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- 3.9. The stopping potential when a frequency of 1.61×1015 Hz is shone on a metal is 3V. (a) What is energy transferred by each photon? (b) Calculate the work function of the metal. (c) Find the Lorentz factor. (d) What is the maximum speed of the ejected electrons?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.Consider a black body of surface area 20.0 cm² and temperature 5000 K. Find the spectral power at 580 nm.
- A 2.0-mW green laser ( λ = 532 nm) shines on a cesium photocathode (Φ =1.95 eV). Assume an efficiency of 10-5 for producing photoelectrons (that is, one photoelectron produced for every 105 incident photons) and determine the photoelectric current(a) Use the appropriate Uncertainty Principle to calculate the linewidth uncertainty in units of Hz, for an optical emission transition that has a lifetime of τ = 10−9 s. (b) Use calculus to show that an emission transition that has a linewidth of ∆f in frequency, has a linewidth in wavelength given by ∆λ = −(λ^2)/c * ∆f (c) What would be the linewidth in nm, of a transition at 600 nm if it had the lifetime given in part (a)?. Find the momentum of a photon in eV/c and in kg·m/s if the wavelength is (a) 400 nm, (b) 1 Å = 0.1 nm, (c) 3 cm, and (d) 2 nm.
- In collection of microscopic oscillators, the temperature is high enough that the ground state and the first two excited states are occupied. Which stands to all the possible energies of the photons emitted by these oscillators: 0.5hoo, ħwo O hwo, 2ħwo O 0.5hwo, 2ħwo Find the values of all the possible energies of photons emitted by such oscillators in eV if the lowest energy photon observed in the vibrational spectrum is 0.039 eV. Possible energies are : eV, eVAn x-ray is modeled by the equation E= (1000V/m)sin(kx - 8.96 *1018t) What is the wavenumber, k, in m-1, of this x-ray?