Solved Problem on Quantum Physics

The surface temperature of the Sun is approximately 5700 K, and the temperature of the human body, under normal conditions, is 36°C. Mark in the spectrum below the approximate wavelengths that correspond to the greatest intensity of radiation emitted by these bodies.

Problem data:

Temperature at the surface of the Sun: T_S = 5700 K;
Human body temperature: t_H = 36°C.

Solution

First, we must convert the human body temperature given in degrees Celsius to Kelvins

\[ \begin{gather} T=t_{C}+273=36+273=309\;\text{K} \end{gather} \]

Wien's Law is given by

\[ \begin{gather} \bbox[#99CCFF,10px] {\lambda_{max}T=2.989\times 10^{-3}\;\text{m.K}} \end{gather} \]

Applying this expression to the Sun (T = T_S = 5700 K)

\[ \begin{gather} \lambda_{max}=\frac{2.989\times 10^{-3}}{5700}\\[5pt] \lambda_{max}=5.24\times 10^{-7}=524\times 10^{-9}\\[5pt] \lambda_{max}=524\;\text{nm} \end{gather} \]

Applying this expression to the human body (T = T_H = 309 K)

\[ \begin{gather} \lambda_{max}=\frac{2.989\times 10^{-3}}{309}\\[5pt] \lambda_{max}=9.67\times 10^{-6}=9670\times 10^{-9}\\[5pt] \lambda_{max}=9670\;\text{nm} \end{gather} \]

Note: The Sun is classified as a yellow star, but the peak emission occurs for the green light in the visible region of the electromagnetic spectrum, light from the Sun has all wavelengths and is, therefore, white light. For the human body the emission peak occurs in the infrared region of the spectrum, invisible to the human eye but which is identified with the heat emitted by the body, due to this heat-sensitive cameras are used to film people in the dark.

Fisicaexe - Physics Solved Problems by Elcio Brandani Mondadori is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License .