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Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of 6000 K. Maximum intensity is emitted at a wavelength of about 4800 Å. If the sun were to cool down from 6000 K to 3000K, then the peak intensity would occur at a wavelength
- a)4800 Å
- b)9600 Å
- c)7200 Å
- d)6400 Å
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Solar radiation emitted by the sun resembles that emitted by a black ...
Explanation:
1. Planck's Law:
Planck's law describes the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. According to Planck's law, the intensity of radiation emitted by a black body is maximum at a certain wavelength, known as the peak wavelength. The peak wavelength is inversely proportional to the temperature of the black body.
2. Relationship between Temperature and Peak Wavelength:
The relationship between the temperature of a black body and the peak wavelength is given by Wien's displacement law:
λ_peak = b/T
where λ_peak is the peak wavelength, T is the temperature, and b is Wien's displacement constant.
3. Given Information:
In this question, it is given that the sun emits radiation resembling that of a black body at a temperature of 6000 K. The peak intensity occurs at a wavelength of 4800 Å (1 Ångstrom = 10^-10 meters).
4. Determining the Peak Wavelength at 3000 K:
To find the peak wavelength at 3000 K, we can use the relationship between temperature and peak wavelength:
λ_peak = b/T
For the initial temperature of 6000 K, we have λ1_peak = 4800 Å. Let's calculate the value of b using this information.
4800 Å = b/6000 K
Simplifying the equation, we find:
b = 4800 Å * 6000 K = 28,800,000 Å K
Now, let's find the peak wavelength at 3000 K using the same value of b:
λ2_peak = 28,800,000 Å K / 3000 K = 9600 Å
Therefore, the peak intensity would occur at a wavelength of 9600 Å if the sun were to cool down from 6000 K to 3000 K.
5. Answer:
The correct answer is option 'B' - 9600 Å.
1. Planck's Law:
Planck's law describes the spectral distribution of electromagnetic radiation emitted by a black body at a given temperature. According to Planck's law, the intensity of radiation emitted by a black body is maximum at a certain wavelength, known as the peak wavelength. The peak wavelength is inversely proportional to the temperature of the black body.
2. Relationship between Temperature and Peak Wavelength:
The relationship between the temperature of a black body and the peak wavelength is given by Wien's displacement law:
λ_peak = b/T
where λ_peak is the peak wavelength, T is the temperature, and b is Wien's displacement constant.
3. Given Information:
In this question, it is given that the sun emits radiation resembling that of a black body at a temperature of 6000 K. The peak intensity occurs at a wavelength of 4800 Å (1 Ångstrom = 10^-10 meters).
4. Determining the Peak Wavelength at 3000 K:
To find the peak wavelength at 3000 K, we can use the relationship between temperature and peak wavelength:
λ_peak = b/T
For the initial temperature of 6000 K, we have λ1_peak = 4800 Å. Let's calculate the value of b using this information.
4800 Å = b/6000 K
Simplifying the equation, we find:
b = 4800 Å * 6000 K = 28,800,000 Å K
Now, let's find the peak wavelength at 3000 K using the same value of b:
λ2_peak = 28,800,000 Å K / 3000 K = 9600 Å
Therefore, the peak intensity would occur at a wavelength of 9600 Å if the sun were to cool down from 6000 K to 3000 K.
5. Answer:
The correct answer is option 'B' - 9600 Å.
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Community Answer
Solar radiation emitted by the sun resembles that emitted by a black ...
From Wien’s displacement law,
= 9600 Å
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Solar radiation emitted by the sun resembles that emitted by a black body at a temperature of 6000 K. Maximum intensity is emitted at a wavelength of about 4800 Å. If the sun were to cool down from 6000 K to 3000K, then the peak intensity would occur at a wavelengtha)4800 Åb)9600 Åc)7200 Åd)6400 ÅCorrect answer is option 'B'. Can you explain this answer?
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