# The energy luminosity of the black body is Re = 10 kW / m2. Determine the wavelength corresponding

The energy luminosity of the black body is Re = 10 kW / m2. Determine the wavelength corresponding to the maximum spectral density of the radiant luminosity of this body.

Re = 10 kW / m ^ 2 = 10,000 W / m ^ 2.
σ = 5.67 * 10 ^ -8 W / m ^ 2 * K ^ 4
λmax -?
According to Wien’s law of displacement, the wavelength that corresponds to the maximum spectral density is determined by the formula: maximum: λmax = 0.0028999 / T.
We find the temperature T according to the Stefon-Boltzmann law: Re = σ * T ^ 4, where Re is the energy luminosity of the black body, σ is the Stefan-Boltzmann constant, T is the absolute temperature. Temperature ТRe = 10 kW / m2.
T ^ 4 = Re / σ.
T = √√ (Re / σ).
λmax = 0.0028999 / √√ (Re / σ).
λmax = 0.0028999 / √√ (10000 W / m ^ 2 / 5.67 * 10 ^ -8 W / m ^ 2 * K ^ 4) = 4.4 * 10 ^ -6 m.
Answer: the wavelength that corresponds to the maximum spectral density, λmax = 4.4 * 10 ^ -6 m.

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