The blackbody radiation from a microwave source has its maximum intensity at a wavelength of 0.792 mm.What is the temperature of the microwave source?
A)3.66 K
B)2.34 K
C)2.73 K
D)4.09 K

Question

Quizplus · Accepted Answer

The temperature of the microwave source can be found using Wien's displacement law, which states that the product of the maximum wavelength ($\lambda_{max}$) of the emitted radiation and the temperature (T) of the black body is a constant. The law is given by $\lambda_{max} T = b$, where $b = 2.898 \times 10^{-3} m \cdot K$. Rearranging for T gives $T = \frac{b}{\lambda_{max}}$. Substituting $\lambda_{max} = 0.792 \times 10^{-3} m$ (since 0.792 mm = 0.792 x 10^-3 m) and $b = 2.898 \times 10^{-3} m \cdot K$, we find $T = \frac{2.898 \times 10^{-3}}{0.792 \times 10^{-3}} = 3.66 K$.

The Blackbody Radiation from a Microwave Source Has Its Maximum