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![### Understanding Radiation Emission of the Human Body at Different Wavelengths
**Question:**
The temperature of the human body is 37°C. At what wavelength is the intensity of radiation emitted by the human body maximum?
**Explanation:**
At a temperature of 37°C (310 K), the human body emits thermal radiation across a spectrum of wavelengths. According to Planck's law and Wien's displacement law, which are crucial in calculating the peak wavelength for thermal radiation emission, we can determine the wavelength at which the intensity of radiation is maximal.
**Key Concept: Wien's Displacement Law**
Wien's Displacement Law states that the wavelength of the peak emission of a blackbody is inversely proportional to its temperature (in Kelvin). This can be expressed with the formula:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where:
- \( \lambda_{\text{max}} \) is the peak emission wavelength,
- \( b \) is Wien's displacement constant, approximately \( 2.897 \times 10^{-3} \text{ m} \cdot \text{K} \),
- \( T \) is the absolute temperature in Kelvin.
**Calculations:**
1. Convert the body temperature from Celsius to Kelvin:
\[ 37^\circ\text{C} = 37 + 273 = 310 \text{ K} \]
2. Insert the values into Wien's displacement law:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3} \text{ m.K}}{310 \text{ K}} \]
\[ \lambda_{\text{max}} \approx 9.34 \times 10^{-6} \text{ m} \]
\[ \lambda_{\text{max}} \approx 9.34 \mu\text{m} \]
**Conclusion:**
The intensity of radiation emitted by the human body is maximum at a wavelength of approximately 9.34 micrometers (μm). This falls within the infrared region of the electromagnetic spectrum, which is why humans and other warm-blooded animals are often visible in infrared imaging devices.](https://content.bartleby.com/qna-images/question/bdf4ad1c-8d6e-4c6e-ab0d-20fae6a9f061/89f345b4-66eb-4b4d-ae30-4b77648584dd/57ycmju_processed.png)
Transcribed Image Text:### Understanding Radiation Emission of the Human Body at Different Wavelengths
**Question:**
The temperature of the human body is 37°C. At what wavelength is the intensity of radiation emitted by the human body maximum?
**Explanation:**
At a temperature of 37°C (310 K), the human body emits thermal radiation across a spectrum of wavelengths. According to Planck's law and Wien's displacement law, which are crucial in calculating the peak wavelength for thermal radiation emission, we can determine the wavelength at which the intensity of radiation is maximal.
**Key Concept: Wien's Displacement Law**
Wien's Displacement Law states that the wavelength of the peak emission of a blackbody is inversely proportional to its temperature (in Kelvin). This can be expressed with the formula:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where:
- \( \lambda_{\text{max}} \) is the peak emission wavelength,
- \( b \) is Wien's displacement constant, approximately \( 2.897 \times 10^{-3} \text{ m} \cdot \text{K} \),
- \( T \) is the absolute temperature in Kelvin.
**Calculations:**
1. Convert the body temperature from Celsius to Kelvin:
\[ 37^\circ\text{C} = 37 + 273 = 310 \text{ K} \]
2. Insert the values into Wien's displacement law:
\[ \lambda_{\text{max}} = \frac{2.897 \times 10^{-3} \text{ m.K}}{310 \text{ K}} \]
\[ \lambda_{\text{max}} \approx 9.34 \times 10^{-6} \text{ m} \]
\[ \lambda_{\text{max}} \approx 9.34 \mu\text{m} \]
**Conclusion:**
The intensity of radiation emitted by the human body is maximum at a wavelength of approximately 9.34 micrometers (μm). This falls within the infrared region of the electromagnetic spectrum, which is why humans and other warm-blooded animals are often visible in infrared imaging devices.
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