Power radiated by black body at temperature T1 is P and it radiates maximum energy at a wavelength 11. If the temperature of the black body is changed from T1 to T2, it radiates max energy at a wavelength of 11/2. The power radiated at T2 is
Correct answer: E. 16P
- A. 2P
- B. 4P
- C. 8P
- D. 6P
- E. 16P
Explanation
The information provided in the image states that:The power radiated by a black body at temperature T₁ is P, and it radiates maximum energy at a wavelength λ₁.When the temperature of the black body changes from T₁ to T₂, it starts radiating maximum energy at a wavelength of λ₁/2.We are asked to find the power radiated at temperature T₂.Key concept:Wein's displacement law states that the wavelength (λ) at which a black body radiates the maximum intensity is inversely proportional to its temperature (T). Mathematically, it can be expressed as:λT = constantwhere the constant is approximately 2.897 x 10^-3 m⋅K.Reasoning:Relating λ₁ and T₁ using Wein's displacement law:λ₁T₁ = constantRelating λ₂ and T₂ using Wein's displacement law:λ₂T₂ = constantWe are given:λ₂ = λ₁/2Substituting the second equation into the first equation:λ₁T₁ = (λ₁/2)T₂Solving for T₂:T₂ = 2T₁Relation between power radiated (P) and temperature (T) for a black body:P ∝ T⁴ (Stefan-Boltzmann law)Taking the ratio of the power radiated at T₂ (P₂) to the power radiated at T₁ (P₁):P₂/P₁ = (T₂⁴ / T₁⁴)Substituting T₂ = 2T₁ from step 5:P₂/P₁ = (2T₁⁴ / T₁⁴) = 2⁴ = 16Therefore, the power radiated at temperature T₂ (P₂) is 16 times the power radiated at temperature T₁ (P₁). This translates to 16P as the answer.
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Classical physics cannot explain blackbody radiation and related observations, leading to Planck’s quantum theory, in which energy is emitted or absorbed in discrete packets. Photons provide the particle model of light, with energy and momentum linked to frequency and wavelength, including the photoelectric effect and its threshold frequency.
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