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HW 1: Radiation, Black Bodies and Planck’s Equation

Question-1

  1. Sketch waves a1, a2 and a3 with wavelengths of 4cm,8cm,12cm4cm, 8cm, 12cm that have traveled the same distance during a 1s interval.

  2. Sketch waves b1, b2 and b3 with frequencies of 4s−1,8s−1,12s−14 s^{-1}, 8 s^{-1}, 12 s^{-1} that have traveled the same distance during a 1s interval.

  3. Order waves of parts 1 and 2 in one list with increasing energies.

  4. What part of electromagnetic spectrum do waves in parts 1 and 2 fall?

  5. Do light waves (in vacuum) with higher frequency travel with speed that is faster? Slower? Or equal to the speed of light waves with lower frequencies?

Question-2

Certain star has a maximum wavelength of 300nm. Estimate the temperature of the surface of the star.

Question-3

Consider a star, a light bulb and a slab of ice; their respective temperatures are 8500 K, 850 K and 275.13 K

  1. Estimate the wavelength at which their radiation energies peak.

  2. Which one would have the highest intensity of radiation? [Tip: intensity is the total energy put out by black body, e.g integral of Eq 1.2 in McQuarrie over all frequencies.]

  3. Which object radiates waves which are visible to us?

Question-4

Consider 75 W light bulb and an 850 W microwave oven. The radiation they emit are 5⋅1025\cdot 10^2 nm and 150⋅106150\cdot10^6 nm. Estimate the number of photons they emit per second. [Tip: 1 Watt is a unit of power measured in J⋅s−1J\cdot s^{-1}]

Question-5

Light of wavelength 350 nm is incident on a metallic surface with work function of 1.9 eV. (a) What is the kinetic energy of ejected electrons? (b) What is the threshold frequency?