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When the wavelength corresponding to maximum emission of radiation is halved, the radiant power of the body becomes
- a)Double
- b)Sixteen times
- c)Half
- d)Four times
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
When the wavelength corresponding to maximum emission of radiation is ...
Concept:
Wien’s displacement law
For a black body emissive spectrum, the wavelength λmax giving the maximum emissive power at a temperature is inversely proportional to the absolute temperature.
λmax = C/T
λmaxT= C
λ1T1 = λ2T2
The radiation energy emitted by a black body per unit time is given by:
Eb = σAT4
The radiation energy emitted by a body per unit area per unit time is given by:
Eb = ϵσT4
Calculation:
E2 = 16 × E1
Most Upvoted Answer
When the wavelength corresponding to maximum emission of radiation is ...
Explanation:
Relationship between wavelength and radiant power:
- The radiant power emitted by a body is directly proportional to the fourth power of the temperature.
- According to Wien's displacement law, the wavelength corresponding to the maximum emission of radiation is inversely proportional to the temperature.
Effect of halving the wavelength:
- When the wavelength corresponding to the maximum emission of radiation is halved, it means that the temperature of the body has increased.
- Since the radiant power is directly proportional to the fourth power of the temperature, halving the wavelength corresponds to an increase in temperature to the power of 4.
Calculation:
- If we increase the temperature by a factor of 2 (halving the wavelength), the radiant power will increase by a factor of 2 to the power of 4, which is 16.
- Therefore, when the wavelength corresponding to maximum emission of radiation is halved, the radiant power of the body becomes sixteen times.
Therefore, the correct answer is option B) Sixteen times.
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When the wavelength corresponding to maximum emission of radiation is halved, the radiant power of the body becomesa)Doubleb)Sixteen timesc)Halfd)Four timesCorrect answer is option 'B'. Can you explain this answer?
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