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total energy density of black body and photoelectric effect

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1. The distribution of energy density for black body or cavity radiation as a function of frequency in a neighborhood of df about f is given by:
Integrate this function between 0 and infinity to find the total energy density.

2. In an experiment to study the photoelectric effect, booms of photons of various wavelengths are incident on a very clean metallic surface in a vacuum.
a) Derive a symbolic formula which gives the energy of the photons as a function of wavelength.
b) Calculate the constant in this formula and calculate the energy of the photons in eV for the wavelengths 800nm, 625nm, and 500 nm

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It finds the total energy density of black body by integration. It also finds the energy of the photons in the photoelectric effect. The solution is detailed and was rated '5/5' by the student who originally posted the questions.

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