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A hot body radiates with peak intensity near frequency nu0 and has emissivity 0.5. If its absolute temperature is doubled, which statement is correct?

1. the maximum-intensity frequency shifts to near 2 nu0
2. the maximum-intensity frequency shifts to near nu0/2
3. the total emitted energy increases by a factor of 16
4. the total emitted energy increases by a factor of 8

Correct answer: the maximum-intensity frequency shifts to near 2 nu0

Solution

By Wien's displacement law nu_peak is proportional to T, so doubling T doubles the peak frequency to ~2 nu0 (total energy rises by 16 only if emissivity is constant, but the peak-frequency statement is the cleanly correct one).

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