Which law explains that maximum spectral... | Agricultural Physics

ICAR JRF Agricultural Physics 29 Jun 2024Shift 1

MCQ (Single Correct) +4 −1

Which law explains that maximum spectral radiant emittance from earth features occurs at a wavelength of about 9.7 um?

(A) . Wien's displacement law

(B) . Stefan-Boltzmann law

(C) . Planck's law

Choose the correct answer from the options given below:

(A) only. Correct (B) only, (B) and (C) only. (A), (B) and (C) only,

Wien's Displacement Law in Remote Sensing:

$$\lambda_{\max} = \frac{b}{T} = \frac{2898\ \mu\text{m}\cdot\text{K}}{T}$$

Application to Terrestrial Features:
For Earth features with average kinetic temperatures around $T \approx 300\text{ K}$ ($27^\circ\text{C}$):

$$\lambda_{\max} = \frac{2898}{300} \approx 9.66\ \mu\text{m} \approx 9.7\ \mu\text{m}$$

Wien's law (A) directly explains why Earth's thermal emission peaks in the thermal infrared atmospheric window around $9.7\ \mu\text{m}$. (Correct answer: Option 1)

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