Explanation Write the expression for the Wein’s displacement law for the maximum wavelength at a temperature. λ max = 2.898 × 10 − 3 m ⋅ K T (I) Here, λ max is the maximum wavelength of emission and T is the temperature. Write the expression for the conversion of the temperature in logarithmic form. T ′ = log T (II) Write the expression for the conversion of the wavelength I logarithmic form. λ ′ = log ( λ max ) (III) Conclusion: For sun ( 5800 K ) : Substitute 5800 K for T in equation (I). λ max = 2.898 × 10 − 3 m ⋅ K 5800 K ≈ 500 × 10 − 9 m ≈ 500 nm Substitute 5800 K for T in equation (II). T ′ = log ( 5800 ) = 3.76 Substitute 500 × 10 − 9 m for λ max in equation (III). λ ' = log ( 500 × 10 − 9 m ) = − 6.30 This wavelength of the sun lies in the visible region. For furnace ( 1900 K ) : Substitute 1900 K for T in equation (I). λ max = 2.898 × 10 − 3 m ⋅ K 1900 K ≈ 1525 × 10 − 9 m ≈ 1 525 nm Substitute 1900 K for T in equation (II). T ′ = log ( 1900 ) = 3.28 Substitute 1525 × 10 − 9 m for λ max in equation (III)

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Chapter 3, Problem 61P

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The plot for λmax and the temperature for the different regions of spectrum.

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