1) The spectral emittance of a radiating cavity is maximal at a wavelength of 32 µm. The temperature is then changed so that the total power radiated in the cavity triples. Calculate the new temperature of the cavity. 2) A proton is moving at a speed of 0.923c. If the kinetic energy is tripled, by how much does the speed increase?
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- 1. The maximum radiance of a blackbody is at wavelength λ = 1.2 µm. a) At what temperature does this occur? b) Estimate the brightness temperature for a grey body at this wavelength if the emissivity coefficient is 0.9. (Use the full formula.) ( hcA square metal plate with a side 0.4m is heated to a temperature of 2000k by passing a current through it. Assuming that it behaves like a blackbody, how much power does the plate radiate under these conditions?) a) What temperature is required for a black body spectrum to peak in the X-ray band? (Assume that E = 1 keV). What is the frequency and wavelength of a 1 keV photon? b) What is one example of an astrophysical phenomenon that emits black body radiation that peaks near 1 keV? c) What temperature is required for a black body spectrum to peak in the gamma-ray band with E = 1 GeV? What is the frequency and wavelength of a 1 GeV photon? d) What is one example of an astrophysical phenomenon that emits black body radiation that peaks at 1 GeV?
- 5) What is the magnitude of the wave number k in region I or III in fig. 5.7? Given that U = 10 MeV, E = 5 MeV and the particle is proton (mc² = 938 MeV). A) 3.455 fm¹ B) 2.501 fm¹ C) 0125 fm D) 0.491 fm¹ of the energy (in 6) The magnitude Energy 0 U E 11 E 2115) What is the magnitude of the wave number k in region I or III in fig. 5.7? Given that U = 10 MeV, E = 5 MeV and the particle is proton (mc² = 938 MeV). A) 3.455 fm¹ B) 2.501 fm¹ C) 0125 fm D) 0.491 fm¹ of the energy (in 6) The magnitude Energy 0 U E 11 E 211Two stars, both of which behave like ideal blackbodies, radiate the same total energy per second. The cooler one has a surface temperature T and 4.0 times the diameter of the hotter star. What is the temperature of the hotter star in terms of T?
- 3. Dimensional analysis can provide insight into Stefan-Boltzmann's law for the radiation from a black body. According to this law the intensity of radiation, in units of J s-' m-², from a body at temperature Tis 1 = GT*, where e is Stefan-Boltzmann's constant. Because black-body radiation can be considered to be a gas of photons, i.e. quantum particles which move with velocity e with typical energies of the order of kT, the intensity I is a function of h, c and kT. Use dimensional analysis to confirm that Iis proportional to 7 and find the dependence of a on h and c.For a body emitting blackbody radiation, the total power emitted is proportional to the 4th power of the body’s absolute temperature:(T in kelvins)and the wavelength of the emitted EM radiation that has the highest intensity is inversely proportional to the body’s absolute temperature according to:( in meters, T in kelvins)Assume an object is emitting blackbody radiation. A body in a room at 300 K is heated to 3,000 K. The wavelength of the most intense EM radiation emitted by the body at 3,000 K is the wavelength of the most intense EM radiation at 300 K.a) For photon, electron and neutror, each having energy E = SD₂V = 50 (1.602 x 10+9y), calculate the de Broglie wavelengths and the frequency of an 6) calculate the de Broglie wavelength of a baseball 0.150kg moving at of weight 150g 100 mph. ( SVA
- If all the energy from a 93 W light bulb is emitted, on average, at 530.0 nm, how many 530.0 nm photons must be emitted each second to account for all 93 W? Planck's constant is 6.6 x 1034 J*s and the speed of light is 3.0 x 10° m/s.The Earth has an average surface temperature of 288K and the Sun has an average surface temperature of 5800K. Assume them to be black bodies. If the only radiation that either black body emitted was at it's peak wavelength how many more photons would Earth need to radiation than receive in order for the climate to be stable.A) Astronomers measure the peak wavelength of a nearby star to be 410 nm. What is the star's temperature? B) How much energy does a single photon of light have at this wavelength? C) An electron bound in an unknown metal requires 1.45E-19 ] of energy under the photoelectric effect to become free of the metal. How much kinetic energy would it have if struck by the photon froft part (b)? D) What is the final speed of the elctron from part (c)?