Physics
Physics
Problem
A white-light source radiates of power equally in two discrete spectral lines: violet light of wavelength and infrared light of wavelength . Assume conversion of electrical energy into these two monochromatic beams and negligible emission at other wavelengths. (i) Show that the energy of a single violet photon is twice the energy of a single infrared photon. (ii) Calculate the number of violet photons and the number of infrared photons emitted by the source per second. (iii) What percentage of the total number of photons emitted per second belong to the violet line?Intuitive explanation
The key insight is that photon energy depends inversely on wavelength through , so shorter wavelengths carry more energy per photon. Since the source splits its power equally between two lines, the line with higher-energy photons must emit fewer photons per second to deliver the same power. You'll use energy conservation and the photon energy formula to count individual photons and find their relative proportions.
Intuitive explanation
The key insight is that photon energy depends inversely on wavelength through , so shorter wavelengths carry more energy per photon. Since the source splits its power equally between two lines, the line with higher-energy photons must emit fewer photons per second to deliver the same power. You'll use energy conservation and the photon energy formula to count individual photons and find their relative proportions.