Thermal radiation law: The wavelength corresponding to maximum monochromatic emissive power varies inversely with absolute temperature according to which law?

Introduction / Context:
Blackbody radiation describes how ideal emitters radiate energy as a function of wavelength and temperature. Several fundamental laws describe different aspects of this emission.

Given Data / Assumptions:

• We consider the wavelength λ_max at which the spectral emissive power is maximum for a given absolute temperature T.
• Emphasis is on the inverse proportionality λ_max * T ≈ constant.

Concept / Approach:
Wien’s displacement law states λ_max * T = b, where b is Wien’s constant. This gives the simple inverse relationship and explains why hotter bodies radiate at shorter peak wavelengths (e.g., the Sun peaks in the visible, a hot stove in the infrared).

Step-by-Step Solution:

Verification / Alternative check:
Apply to two temperatures to see the shift: doubling T halves λ_max, confirming the inverse proportionality.

Why Other Options Are Wrong:

• Kirchhoff’s law: not about peak wavelength.
• Stefan–Boltzmann: total power, proportional to T^4, not spectral peak.
• Planck’s law: full spectrum formula; the inverse result emerges from differentiating Planck’s law, but the named simple relation is Wien’s.

Common Pitfalls:
Confusing total emissive power (Stefan–Boltzmann) with the wavelength of maximum emission (Wien’s).

Final Answer:
Wien’s displacement law