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A small body has a total emissive power of 4.5 kW/m2. Determine the wavelength of emission maximum
- a)8.46 micron m
- b)7.46 micron m
- c)6.46 micron m
- d)5.46 micron m
Correct answer is option 'D'. Can you explain this answer?
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A small body has a total emissive power of 4.5 kW/m2. Determine the wa...
(Wavelength) max t = 2.8908 * 10 -3.
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A small body has a total emissive power of 4.5 kW/m2. Determine the wa...
Given: Total emissive power (E) = 4.5 kW/m²
To find: Wavelength of emission maximum
Explanation:
1. Wien's displacement law
According to Wien's displacement law, the wavelength of maximum emission (λmax) from a black body is inversely proportional to its absolute temperature (T).
λmax ∝ 1/T
Here, we are not given the temperature of the body. So, we cannot use this formula directly.
2. Stefan-Boltzmann law
The total emissive power (E) of a black body is given by the Stefan-Boltzmann law:
E = σT⁴
where σ is the Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²K⁴).
We can rearrange this equation to get T in terms of E:
T = (E/σ)⁰⁻⁴
3. Substituting values
Now we can substitute the given value of E to get T:
T = (4.5×10³/5.67×10⁻⁸)⁰⁻⁴ = 694.5 K
4. Using Wien's displacement law
Now we can use Wien's displacement law to find the wavelength of maximum emission:
λmax = b/T
where b is Wien's displacement constant (2.898×10⁻³ mK).
Substituting the value of T, we get:
λmax = 2.898×10⁻³/694.5 = 4.17×10⁻⁶ m = 4.17 microns
Therefore, the correct option is (D) 5.46 micron m (None of the given options match the calculated value of λmax. The closest option is 5.46 microns, which is not correct.)
To find: Wavelength of emission maximum
Explanation:
1. Wien's displacement law
According to Wien's displacement law, the wavelength of maximum emission (λmax) from a black body is inversely proportional to its absolute temperature (T).
λmax ∝ 1/T
Here, we are not given the temperature of the body. So, we cannot use this formula directly.
2. Stefan-Boltzmann law
The total emissive power (E) of a black body is given by the Stefan-Boltzmann law:
E = σT⁴
where σ is the Stefan-Boltzmann constant (5.67×10⁻⁸ W/m²K⁴).
We can rearrange this equation to get T in terms of E:
T = (E/σ)⁰⁻⁴
3. Substituting values
Now we can substitute the given value of E to get T:
T = (4.5×10³/5.67×10⁻⁸)⁰⁻⁴ = 694.5 K
4. Using Wien's displacement law
Now we can use Wien's displacement law to find the wavelength of maximum emission:
λmax = b/T
where b is Wien's displacement constant (2.898×10⁻³ mK).
Substituting the value of T, we get:
λmax = 2.898×10⁻³/694.5 = 4.17×10⁻⁶ m = 4.17 microns
Therefore, the correct option is (D) 5.46 micron m (None of the given options match the calculated value of λmax. The closest option is 5.46 microns, which is not correct.)
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