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Step-by-Step Explanation
1. Understanding the Color Change of Heated Iron
As iron is heated, it begins to glow. The color it emits shifts from dull red to reddish yellow and finally appears white hot at very high temperatures. This change directly relates to how the peak wavelength ($\lambda_m$) of emitted radiation depends on the temperature of the object.
2. Wien's Displacement Law
Wien's Displacement Law states that the product of the temperature ($T$) of a radiating body and the wavelength ($\lambda_m$) at which it emits the most intensely is constant:
$ \lambda_m \, T = \text{constant} $
Rearranging this gives:
$ \lambda_m = \frac{\text{constant}}{T} $
This means that as the temperature of an object increases, its peak emission wavelength ($\lambda_m$) decreases. In other words, the most intense color of the emitted light shifts to shorter wavelengths as the temperature increases.
3. Linking Color to Wavelength
Dull red glow: At lower temperatures, the peak emission is in the longer wavelength region of visible light (toward the red end).
Reddish yellow: As the temperature rises, the peak shifts to slightly shorter wavelengths, producing a brighter, more yellowish glow.
White hot: At very high temperatures, the iron emits a range of wavelengths across the visible spectrum. When all wavelengths combine, the object appears white to our eyes.
4. Conclusion
Therefore, the color change of a piece of iron as it is heated can be explained using Wien's Displacement Law. The increasing temperature causes the peak wavelength of emission to shift progressively from the red to the yellow region, and eventually so many wavelengths are emitted that the iron appears white hot.
