Chapter 33, Problem 30P

To determine

The wavelength at the peak of the blackbody radiation distribution.

Answer to Problem 30P

The wavelength at the peak of the blackbody radiation distribution is $1.1\times {10}^{-3}\text{ m}$

Explanation of Solution

Given:

Temperature at the peak of the blackbody radiation is $2.7\text{ K}$

Formula used:

According to the Wien’s law,

  ${\lambda }_{\text{P}}\text{T = }\alpha$

Calculation:

The wavelength at the peak of the blackbody radiation is

  $\begin{array}{c}{\lambda }_{\text{P}}\text{T = 2}\text{.90}\times {\text{10}}^{-3}\text{ m}\cdot \text{K}\\ {\lambda }_{\text{P}}\text{=}\frac{\text{2}\text{.90}\times {\text{10}}^{-3}\text{ m}\cdot \text{K}}{\text{T}}\\ \text{=}\frac{\text{2}\text{.90}\times {\text{10}}^{-3}\text{ m}\cdot \text{K}}{2.7\text{ K}}\\ {\lambda }_{\text{P}}\text{=}1.1\times {10}^{-3}\text{ m}\end{array}$

Conclusion:

Thus, the wavelength at the peak of the blackbody radiation distribution at $2.7\text{ K}$ is $1.1\times {10}^{-3}\text{ m}$