Estimate the wavelength corresponding to maximum emission fr

Estimate the wavelength corresponding to maximum emission from each of the following surfaces. the sun. whose temperature is known to be around 5800 K, a tungsten filament at 3000 K. and a heated metal plate at 500 K. Estimate the fraction of emission in each case within the visible range of wavelength, A = 0.4 - 0.7 pm. Which surface, (a, b or c) will not look bright and why? (Given, Wien\'s Displacement Law: lambda_max T = 2898 mm middot K)

Solution

a) Using wien displacement law

     lambda * 5800 = 2.898 mm K

     lambda = 0.5 * 10^-6 m

b) Using wien displacement law

     lambda * 3000 = 2.898 mm K

     lambda = 0.966 * 10^-6 m

c) Using wien displacement law

     lambda * 500 = 2898 mm K

     lambda = 5.796 * 10^-6 m

d) Fractional Range for sun   = 0.5 - 0.4 / 0.5 = 0.2

    Fractional Range for tungsten = 0.7 - 0.4 / 0.966 = 0.31

    Fractional Range for heat metal = 0.7 - 0.4 / 5.796 = 0.05175

e) Heat Metal will not look bright because its wavelength emitted is in infrared range.