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Chapter 14: Problem 59

If a blackbody is radiating at \(T=1650 \mathrm{K},\) at what wavelength is the maximum intensity?

Short Answer

Expert verified
Answer: The maximum intensity for a blackbody at a temperature of 1650 K is radiated at a wavelength of approximately 1.756 x 10^-6 m or 1756 nm.

Step by step solution

01

Understand Wien's Displacement Law

Wien's Displacement Law formula states that the product of the maximum wavelength (λ_max) and the temperature (T) of a blackbody is a constant, represented by the symbol b: λ_max * T = b Here, b is Wien's displacement constant, which is equal to 2.898 x 10^-3 m*K.
02

Find the maximum wavelength (λ_max)

Now that we have the temperature (T) and Wien's constant (b), we can find the maximum wavelength (λ_max) as follows: λ_max = b / T Now, plug in the values for b (2.898 x 10^-3 m*K) and T (1650 K): λ_max = (2.898 x 10^-3 m*K) / (1650 K)
03

Calculate the result

After dividing the values, we get: λ_max = 1.756 x 10^-6 m This value is the maximum wavelength at which the maximum intensity is radiated by the blackbody. So, the maximum intensity for a blackbody at a temperature of 1650 K is radiated at a wavelength of approximately 1.756 x 10^-6 m or 1756 nm.

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Most popular questions from this chapter

Small animals eat much more food per kg of body mass than do larger animals. The basal metabolic rate (BMR) is the minimal energy intake necessary to sustain life in a state of complete inactivity. The table lists the BMR, mass, and surface area for five animals. (a) Calculate the BMR/kg of body mass for each animal. Is it true that smaller animals must consume much more food per kg of body mass? (b) Calculate the BMR/m" of surface area. (c) Can you explain why the BMR/m \(^{2}\) is approximately the same for animals of different sizes? Consider what happens to the food energy metabolized by an animal in a resting state.
If \(4.0 \mathrm{g}\) of steam at \(100.0^{\circ} \mathrm{C}\) condenses to water on a burn victim's skin and cools to \(45.0^{\circ} \mathrm{C},\) (a) how much heat is given up by the steam? (b) If the skin was originally at $37.0^{\circ} \mathrm{C},$ how much tissue mass was involved in cooling the steam to water? See Table 14.1 for the specific heat of human tissue.
(a) What thickness of cork would have the same R-factor as a 1.0 -cm thick stagnant air pocket? (b) What thickness of tin would be required for the same R-factor?
Compute the heat of fusion of a substance from these data: \(31.15 \mathrm{kJ}\) will change \(0.500 \mathrm{kg}\) of the solid at \(21^{\circ} \mathrm{C}\) to liquid at \(327^{\circ} \mathrm{C},\) the melting point. The specific heat of the solid is \(0.129 \mathrm{kJ} /(\mathrm{kg} \cdot \mathrm{K})\).
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