What is being asked?

The question asks which law correctly gives the spectrum of radiation emitted by the Earth in the infra-red region.

Since the Earth emits thermal radiation, we should identify the law that gives the distribution of intensity with wavelength/frequency.

Check each option

Option A: Rayleigh–Jeans law

This gives the blackbody spectral distribution only as a classical approximation, valid mainly at long wavelengths. It is not the correct general law for the spectrum.

Option B: Planck's law of radiation

Planck’s law gives the complete blackbody spectrum: $I(\lambda, T) = \frac{2\pi hc^2}{\lambda^5}\frac{1}{e^{hc/(\lambda kT)}-1}$ This is the correct law for the spectral distribution of thermal radiation at all wavelengths.

Option C: Stefan's law of radiation

Stefan’s law gives only the total power radiated per unit area: $E = \sigma T^4$ It does not give the spectrum.

Option D: Wien's law

Wien’s displacement law gives only the wavelength of maximum emission: $\lambda_{\max} T = b$ It tells us where the peak lies (for Earth, in infra-red), but it does not give the full spectrum.

Conclusion

Since the question asks for the law that correctly gives the spectrum, the correct answer is: $\boxed{\text{B: Planck's law of radiation}}$

Compare with stored answer

Stored correct answer: D

My derived answer is B. Hence, I disagree with the stored answer.

Likely reason: if the question were asking which law shows that Earth radiates in the infra-red region, then Wien’s displacement law would identify the peak wavelength in IR. But for the spectrum itself, the correct law is Planck’s law.