Wavelength of thermal radiation “The wavelength associated with peak emission depends only on temperature and not on the material.” Evaluate this statement.

Introduction / Context:
Radiative heat transfer involves spectral distributions that depend on temperature and surface properties. A common exam theme is differentiating material effects on emissive power from the temperature dependence of the peak wavelength.

Given Data / Assumptions:

• Thermal radiation from opaque bodies in the infrared–visible bands.
• Interest in the wavelength of maximum emission (peak of the spectrum).

Concept / Approach:
Wien’s displacement law states that the wavelength at which the spectral emissive power is maximum varies inversely with absolute temperature: λ_max * T ≈ constant. While the magnitude of emission (emissivity) depends on material and surface condition, the position of the peak is governed primarily by temperature for a blackbody and closely follows temperature for many real surfaces.

Step-by-Step Solution:
Recognize the claim refers to “wavelength of the radiation emitted,” interpreted as peak wavelength.Apply Wien’s displacement: λ_max = b / T, where b is a constant.Material alters emissivity and spectral shape, but the dominant peak location tracks temperature; thus, the statement is effectively true in the sense of peak wavelength.

Verification / Alternative check:
As temperature increases, thermal glow shifts from infrared toward visible (red, then white), consistent with λ_max shifting to shorter wavelengths independently of the specific material.

Why Other Options Are Wrong:
Limiting validity to metals, vacuum, or gases is unnecessary; the temperature–peak relation is general. Declaring “False” confuses spectral emissivity magnitude (material-dependent) with λ_max (temperature-dependent).

Common Pitfalls:
Interpreting the statement to mean the entire spectrum is identical across materials; only the peak position follows Wien’s law strictly for blackbody reference, while real surfaces approximate it.

Final Answer:
True