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If the temperature of a radiating body is 1500°C, the wavelength at which the maximum radiant energy occurs:
- a)2.8 µm
- b)1.63 µm
- c)1 µm
- d)20.8 µm
Correct answer is option 'B'. Can you explain this answer?
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If the temperature of a radiating body is 1500°C, the wavelength at w...
The wavelength at which the human body radiates maximum energy is 12 microns. Most of the radiation that the human body emits is in the infrared region. This region has a wavelength that is much more than that of the red visible light and varies between 0.75 to 1,000 microns.
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If the temperature of a radiating body is 1500°C, the wavelength at w...
To determine the wavelength at which the maximum radiant energy occurs, we can use Wien's displacement law.
1. Understanding Wien's Displacement Law:
- Wien's displacement law states that the wavelength (λ) at which the maximum radiant energy occurs is inversely proportional to the temperature (T) of the radiating body.
- Mathematically, the equation is given by: λ_max = b / T, where b is a constant known as Wien's displacement constant.
2. Applying Wien's Displacement Law:
- Given that the temperature of the radiating body is 1500°C, we need to convert it to Kelvin as the formula requires temperature in Kelvin.
- To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature.
- So, the temperature in Kelvin is 1500 + 273.15 = 1773.15 K.
3. Calculating the wavelength at which the maximum radiant energy occurs:
- Now, we can apply Wien's displacement law to find the wavelength.
- The equation is: λ_max = b / T.
- The value of Wien's displacement constant (b) is approximately 2.898 × 10^(-3) m·K.
- Plugging in the values, we get: λ_max = (2.898 × 10^(-3) m·K) / (1773.15 K).
- Simplifying the equation, we find: λ_max ≈ 1.63 µm.
4. Final Answer:
- Therefore, the wavelength at which the maximum radiant energy occurs for a radiating body with a temperature of 1500°C is approximately 1.63 µm.
- Hence, the correct answer is option 'B'.
1. Understanding Wien's Displacement Law:
- Wien's displacement law states that the wavelength (λ) at which the maximum radiant energy occurs is inversely proportional to the temperature (T) of the radiating body.
- Mathematically, the equation is given by: λ_max = b / T, where b is a constant known as Wien's displacement constant.
2. Applying Wien's Displacement Law:
- Given that the temperature of the radiating body is 1500°C, we need to convert it to Kelvin as the formula requires temperature in Kelvin.
- To convert from Celsius to Kelvin, we add 273.15 to the Celsius temperature.
- So, the temperature in Kelvin is 1500 + 273.15 = 1773.15 K.
3. Calculating the wavelength at which the maximum radiant energy occurs:
- Now, we can apply Wien's displacement law to find the wavelength.
- The equation is: λ_max = b / T.
- The value of Wien's displacement constant (b) is approximately 2.898 × 10^(-3) m·K.
- Plugging in the values, we get: λ_max = (2.898 × 10^(-3) m·K) / (1773.15 K).
- Simplifying the equation, we find: λ_max ≈ 1.63 µm.
4. Final Answer:
- Therefore, the wavelength at which the maximum radiant energy occurs for a radiating body with a temperature of 1500°C is approximately 1.63 µm.
- Hence, the correct answer is option 'B'.
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If the temperature of a radiating body is 1500°C, the wavelength at which the maximum radiant energy occurs:a)2.8 µmb)1.63 µmc)1 µmd)20.8 µmCorrect answer is option 'B'. Can you explain this answer?
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