Wien's displacment law expresses relation between

Options

A. colour of light and temperature
B. wavelength and temperature
C. radiation energy and wavelength
D. wavelength corresponding to maximum energy and temperature

Explanation

To solve the question regarding Wien's Displacement Law, we will analyze the law and its implications step by step.

### Step 1: Understanding Wien's Displacement Law
Wien's Displacement Law states that the wavelength at which the emission of a black body spectrum 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 known as Wien's displacement constant.

### Step 2: Identifying the Variables
In the equation \( \lambda_{max} \cdot T = b \):
- \( \lambda_{max} \) is the wavelength corresponding to the maximum intensity of radiation emitted by a black body.
- \( T \) is the absolute temperature of the black body in Kelvin.
- \( b \) is a constant approximately equal to \( 2.898 \times 10^{-3} \, \text{m} \cdot \text{K} \).

### Step 3: Relating Wavelength and Temperature
From the law, we can see that as the temperature (T) increases, the wavelength (λ_max) corresponding to the maximum emission decreases. This implies a direct relationship between temperature and the wavelength of emitted radiation.

### Step 4: Conclusion
Based on the explanation of Wien's Displacement Law, the correct relation expressed by the law is between the wavelength corresponding to maximum energy and temperature. Therefore, the answer to the question is:

**Wien's Displacement Law expresses the relation between wavelength corresponding to maximum energy and temperature.**

### Final Answer:
The correct option is D: Wavelength corresponding to maximum energy and temperature.

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