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

Options

A. Wien’s law
B. Rayleigh-Jeans law
C. Planck’s law of radiation
D. Stefan’s law of radiation

Explanation

To solve the question regarding the Earth's radiation in the infrared region of the spectrum, we can follow these steps:

### Step 1: Understand the Question
The question asks which law describes the radiation of the Earth in the infrared region of the spectrum.

**Hint:** Identify the key terms in the question, such as "radiates," "infrared region," and "spectrum."

### Step 2: Recall Relevant Laws
The two primary laws that describe the radiation of bodies based on their temperature are Stefan-Boltzmann Law and Wien's Displacement Law.

**Hint:** Think about the laws related to black body radiation and how they relate to temperature and wavelength.

### Step 3: Define Wien's Displacement Law
Wien's Displacement Law states that the wavelength at which the emission of radiation is maximized (λ_max) is inversely proportional to the absolute temperature (T) of the black body. Mathematically, it can be expressed as:
\[ \lambda_{max} \cdot T = b \]
where \( b \) is a constant (Wien's displacement constant).

**Hint:** Remember that this law helps in determining the peak wavelength of radiation emitted by a body at a given temperature.

### Step 4: Relate to Earth's Radiation
The Earth, being a relatively cool body compared to the sun, radiates primarily in the infrared region of the spectrum. This is consistent with Wien's Law, as the temperature of the Earth leads to a peak emission in the infrared range.

**Hint:** Consider how the temperature of the Earth affects the wavelength of the radiation it emits.

### Step 5: Conclude the Answer
Based on the understanding of Wien's Displacement Law and its application to the Earth's radiation, we conclude that the correct law that describes the Earth's radiation in the infrared region is Wien's Law.

**Final Answer:** The spectrum is correctly given by Wien's Law.

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