Q270 · Practice questionSimple familiar3 marks
QUESTION 270 (3 marks)
A student models a heated cavity using a classical model that lets each electromagnetic mode exchange energy continuously. It predicts an unbounded increase in emitted energy at very short wavelengths, unlike the observed finite spectrum.
a)[3 marks]
Explain the difficulty with this classical prediction and how Planck extquotesingle s quantisation assumption addresses it.
WORKED SOLUTION
3 marksPractice marking scheme
ANSWER
(a) The prediction disagrees with the finite short-wavelength spectrum. Planck allowed energy exchange in multiples of ; high-frequency quanta require more energy and are less readily excited at a fixed temperature.
Worked solution
(a) The observed spectrum falls toward zero at sufficiently short wavelengths. Quantised exchanges mean that exciting a high-frequency mode requires a larger minimum energy. This changes the energy distribution and removes the classical short-wavelength divergence.
Equivalent physically justified methods, alternative valid sketches and consistent units accepted.
Accept sensible significant figures and consistent rounding from stated constants.
Part a: Identify the disagreement between divergence and the finite observed spectrum.
Part a: State quantised exchanges in multiples of hf.
Part a: Link the larger high-frequency energy requirement to suppression of the classical divergence.
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