Assignment 1: Blackbody Radiation

Assignment 1: Blackbody radiationDue date: 7 September 2009, 11 am7. Show that for very large wavelengths λ, Plank’s formula for spectral radiance,reduces to the Rayleigh-Jeans formula,ρ (λ) = 8πhcλ 5 1exp (hc/λkT ) − 1 , (4)ρ(λ) = 8π kT. (5)λ4 (Note that Rayleigh-Jeans or Plank’s formulas can express the spectral densities eitherin terms of frequency or wavelength. Refer to the approach followed in Question 5.)8. A tuning fork has a natural frequency of 500 Hz and its total vibrational energy is0.04 J. An atom emits orange light at a frequency of 5.00×10 14 Hz and has an energy of2.0 eV. Which of these systems is more likely to exhibit quantum graininess? Supportyou answer quantitatively.Chapter 1 of Eisberg and Resnick. 2