The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Options

A. Rayleigh Jeans law
B. Plank's law of radiation
C. Stefan's law of radiation
D. Wien's law

Explanation

To solve the question regarding the spectrum in which the Earth radiates, we need to analyze the laws of thermal radiation and identify which one applies to the infrared region.

### Step-by-Step Solution:

1. **Understanding Thermal Radiation**:
- All objects emit radiation based on their temperature. The spectrum of this radiation can be described by several laws in physics.

2. **Identify the Relevant Laws**:
- **Stefan-Boltzmann Law**: This law states that the total energy radiated per unit surface area of a black body per unit time is directly proportional to the fourth power of the black body's absolute temperature (T^4).
- **Planck's Law**: This law describes the electromagnetic radiation emitted by a black body in thermal equilibrium at a definite temperature, providing a formula for the intensity of radiation at different wavelengths.
- **Wien's Displacement Law**: This law states that the wavelength at which the emission of a black body spectrum is maximized is inversely proportional to the temperature of the body. It can be mathematically expressed as λ_max = b/T, where b is Wien's displacement constant.
- **Rayleigh-Jeans Law**: This law describes the spectral radiance of electromagnetic radiation at all wavelengths from a black body at a given temperature, but it fails at short wavelengths.

3. **Determine the Region of Interest**:
- The question specifies that the Earth radiates in the infrared region of the spectrum. The infrared region corresponds to longer wavelengths (approximately 700 nm to 1 mm).

4. **Applying Wien's Displacement Law**:
- According to Wien's Displacement Law, as the temperature of an object decreases, the peak wavelength of the emitted radiation increases. Since the Earth has a relatively low temperature compared to hotter bodies (like the Sun), it emits most of its radiation in the infrared region.

5. **Conclusion**:
- Therefore, since the Earth radiates primarily in the infrared region, the spectrum is correctly described by **Wien's Displacement Law**.

### Final Answer:
The spectrum in which the Earth radiates in the infrared region is given by **Wien's Displacement Law**.

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