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Q12E

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Found in: Page 93

### Modern Physics

Book edition 2nd Edition
Author(s) Randy Harris
Pages 633 pages
ISBN 9780805303087

# At what wavelength does the human body emit the maximum electromagnetic radiation? Use Wien's law from Exercise 14 and assume a skin temperature of ${{70}}^{{\circ }}{F}$

The wavelength corresponds to the maximum electromagnetic radiation emitted by the human body is $9.848\mu m$ .

See the step by step solution

## Step 1: Given data

Skin temperature $=70°\text{F}$

## Step 2: Formula used

Wein's law can be expressed in terms of temperature (T) and maximum wavelength ( ${{\lambda }}_{max}$) such that,

${{\lambda }}_{max}{T}{=}{2}{.}{898}{×}{{10}}^{-3}{\text{mK}}$

## Step 3: Calculation using Wien's law

Convert the Fahrenheit temperature to Kelvin, such that

$\begin{array}{rcl}T& =& \left(\left(70-32\right)×\frac{5}{9}\right)°C+273.15K\\ T& =& 294.26\text{K}\\ & & \end{array}$

Using Wein's law

${\lambda }_{\mathrm{max}}T=2.898×{10}^{-3}\text{mK}\phantom{\rule{0ex}{0ex}}{\lambda }_{\mathrm{max}}=\frac{2.898×{10}^{-3}\text{mK}}{294.26K}\phantom{\rule{0ex}{0ex}}{\lambda }_{\mathrm{max}}=9.848×{10}^{-6}\text{m}\left(\frac{1\mu \text{m}}{{10}^{-6}\text{m}}\right)\phantom{\rule{0ex}{0ex}}{\lambda }_{\mathrm{max}}=9.848\mu \text{m}\phantom{\rule{0ex}{0ex}}$

## Step 4: Conclusion

The wavelength which corresponds to the maximum electromagnetic radiation emitted by the human body is $9.848\mu m$.