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SOLUTIONS TO PROBLEMS ON SHEET ONE
QUANTIZATION OF ENERGY
(1a) Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all radiation incident upon it and re-radiates energy which is characteristic of this radiating system only, not dependent upon the type of radiation which is incident upon it. The radiated energy can be considered to be produced by standing wave or resonant modes of the cavity which is radiating. The amount of radiation emitted in a given frequency range should be proportional to the number of modes in that range. The best of classical physics suggested that all modes had an equal chance of being produced, and that the number of modes went up proportional to the square of the frequency. And inversely proportional to the square of wavelength. Hence according to classical physics energy radiated by blackbody approaches infinity as wavelength approaches zero.
(1b) It was Max Planck that solved this problem in 1900. He suggested that each wave has an intrinsic, associated energy. Waves with smaller wavelengths (and therefore higher frequencies) have higher energies. He gave the following equation to determine the energy of a wave:
Energy of a wave = (Planck's constant) * (Frequency of the wave)
This idea is familiar to us today, we know that x-rays have more energy than rays of light, which in turn are more powerful than radio waves. These are all examples of electromagnetic radiation - but with different frequencies, and therefore, according to Planck's idea, different energies
(1c) 'ultraviolet catastrophe', in which ...
With good explanations and calculations, the problems are solved.