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A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U₁, at wavelength 500 nm is U₂, and that at 1000 nm is U₃. Wien's constant, b = 2.88 × 10⁶ nmK. Which of the following is correct?
- U₁ = 0
- U₃ = 0
- U₁ > U₂
- U₂ > U₁
Correct answer: U₁ > U₂
Solution
Using Wien's displacement law, the peak wavelength for the black body is λ_max = b/T = 500 nm. Radiation intensity decreases as we move away from the peak wavelength. Since 250 nm is closer to 500 nm than 1000 nm, U₁ > U₂, and U₃ is much smaller.
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