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The peak wavelength of radiation emitted by a black body at a temperature of 2000 K is 1.45 um. If the peak wavelength of emitted radiation changes to 2.90 um, then the temperature (in K) of the black body is
  • a)
    500
  • b)
    1000
  • c)
    4000
  • d)
    8000
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The peak wavelength of radiation emitted by a black body at a temperat...
λmT = constant
2000 × 1.45 = 2.9 × T
T=1000
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Most Upvoted Answer
The peak wavelength of radiation emitted by a black body at a temperat...
Given:
Temperature, T1 = 2000 K
Peak wavelength, λ1 = 1.45 μm
New peak wavelength, λ2 = 2.90 μm

To find:
Temperature, T2

Formula used: Wien's displacement law
λmaxT = constant, where constant = 2.898 × 10^-3 mK

Calculation:
Using Wien's displacement law, we have:
λ1T1 = λ2T2
(1.45 × 10^-6 m)(2000 K) = (2.90 × 10^-6 m)T2
T2 = (1.45/2.90)T1
T2 = 0.5T1
T2 = 0.5(2000 K)
T2 = 1000 K

Therefore, the temperature of the black body is 1000 K. Answer: Option B.
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