Statement I: As the temperature of the black body increases, the wavelength at which the spectral intensity `(E_lamda)` is maximum decreases.
Statement II: The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.

Options

A. Statement I is true, Statement II is true and Statement II is the correct explanation for statement I.
B. Statement I is true, statement II is true and statement II NOT the correct explanation for Statement I
C. Statement I is true, Statement II is false.
D. Statement I is false, statement II is true.

Explanation

To solve the question, we need to analyze both statements regarding the behavior of a black body in relation to temperature and wavelength.

### Step 1: Understand Statement I
Statement I claims that as the temperature of a black body increases, the wavelength at which the spectral intensity is maximum decreases.

**Explanation:** According to Wien's Displacement Law, the wavelength (λ_max) at which the spectral intensity is maximum is inversely proportional to the absolute temperature (T) of the black body. This can be expressed mathematically as:

\[ \lambda_{max} \propto \frac{1}{T} \]

This means that as the temperature (T) increases, the wavelength (λ_max) decreases. Thus, Statement I is **correct**.

### Step 2: Understand Statement II
Statement II states that the wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.

**Explanation:** This statement contradicts Wien's Displacement Law. According to the law, the relationship is:

\[ \lambda_{max} \cdot T = b \]

where \(b\) is a constant. This implies that:

\[ \lambda_{max} \propto \frac{1}{T} \]

Thus, the wavelength is **not** proportional to the fourth power of the absolute temperature. Therefore, Statement II is **false**.

### Conclusion
Based on the analysis:
- Statement I is true.
- Statement II is false.

The correct answer is that Statement I is true and Statement II is false.

### Final Answer
**Statement I is true, and Statement II is false.**

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