Abstract

When the temperature of a black body is such that the maximum spectral efficiency of production of radiant energy occurs a t a given wave-length there also occurs at that wave-length, both the maximum spectral rate of production and the maximum spectral efficiency of production of photons. The particular wave-length involved is the effective wave-length for the total radiation, which is defined as the wave-length at which, for a given temperature, the percentage rate of increase in spectral radiancy with temperature is the same as for the total radiation from the black body source.

© 1939 Optical Society of America

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References

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  1. Frank Benford, “Laws and Corollaries of the Black Body,” J. Opt. Soc. Am. 29, 92 (1939).
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1939 (1)

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Equations (8)

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λ T m = 3652 μ K ° ,
d / d T [ A / T 4 ( e x - 1 ) ] = 0 ,
1 - x / 4 - e - x = 0 ,
whence             x = 3.9207
and             λ T m = h c / ( 3.9207 k ) = 3652 μ K ° .
λ e T = h c / ( 3.9207 k ) = λ T m
[ T λ d R λ d T ] λ e = T d d T = 4 ,
ν / T m = 3.9207 k / h = 8.2077 × 10 10 1 / ( sec. K ° ) .