Question

Consider the Sun and the Earth as blackbodies at $6000~\text{K}$ and $300~\text{K}$ temperatures, respectively. Which of the following statement(s) is/are INCORRECT?

• A. Sun emits maximum energy at $9.3~\mu\text{m}$
• B. Sun does not emit energy at microwave
• C. The wavelengths of the energies emitted by the Sun are a sub-set of the wavelengths emitted by the Earth
• D. Earth does not emit energy at green wavelength

Hint:

Wien’s law gives the peak: $\lambda_{\max}[\mu\text{m}]\approx \dfrac{2897}{T[\text{K}]}$. Blackbodies emit at {all} wavelengths; what changes dramatically is the magnitude.

Answer 1

The Correct Option is A

Use Wien’s displacement law: $\lambda_{\max}=\dfrac{b}{T}$ with $b\approx 2897~\mu\text{m}.\text{K}$.
- For the Sun ($T\!=\!6000$ K): $\lambda_{\max}\approx \dfrac{2897}{6000}\approx 0.48~\mu$m (visible blue–green). Thus statement (A) claiming $9.3~\mu$m is incorrect.
- For the Earth ($T\!=\!300$ K): $\lambda_{\max}\approx \dfrac{2897}{300}\approx 9.66~\mu$m (thermal IR).
(B) Incorrect. A blackbody emits over all wavelengths ($\lambda>0$); the Sun’s microwave emission is extremely small but non-zero. Saying it “does not emit” is wrong.
(C) Incorrect. Neither body’s emission wavelengths are a subset of the other—both blackbodies emit over a continuous spectrum. The Sun peaks at shortwave (UV–VIS–NIR), Earth at longwave (thermal IR).
(D) Considered correct in remote-sensing context. The Earth’s thermal emission at $\sim0.55~\mu$m (green) is negligible (far from its $9$–$10~\mu$m peak) and is commonly treated as no emission in practice, hence (D) is not marked incorrect.