Q182 · Practice questionComplex familiar6 marks
QUESTION 182 (6 marks)
The graph shows two black-body spectra, each normalised separately so its own peak equals one. Their peak wavelengths are for A and for B. Use .
a)[2 marks]
Determine the temperature of each source.
b)[2 marks]
Determine the ratio of individual photon energies at the two peak wavelengths, .
c)[2 marks]
A student says the equal plotted peak heights prove equal emitted peak spectral intensities. Explain why the graph cannot support that claim.
WORKED SOLUTION
6 marksPractice marking scheme
ANSWER
(a) ; . (b) . (c) The two spectra have different, unspecified normalisation factors, so their absolute intensities cannot be compared.
Worked solution
(a) Wien's law gives . Thus and .
(b) for an individual photon, so . This is not a comparison of total emitted energies.
(c) Each curve has been divided by its own maximum. Equal plotted peaks are a consequence of the scaling, not evidence of equal physical intensity. Absolute intensity or the normalisation factors would be needed.
Equivalent physically justified methods and consistent equivalent units accepted.
Displayed decimals are model answers; accept appropriate significant figures and consistent rounding from stated constants.
Part a: Apply Wien law and convert the first peak wavelength.
Part a: Calculate the second temperature.
Part b: Use photon energy inversely proportional to wavelength.
Part b: Calculate the energy ratio.
Part c: Identify that each curve uses its own scaling factor.
Part c: Explain why absolute peak intensities cannot be inferred.
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