Mark out the correct statement with respect to thermal radiations emitted by a black body

Options

A. At a given temperature, , energy is distributed non - uniformly among different wavelengths
B. As temperature of body is increased , energy content of all wavelengths decreases
C. The product of `E_lamda` (spectral energy) with `D_(lamda)` (spectral width) , for all equal `Deltalamda'` is the same
D. The thermal radiation emitted by a hot body is a discrete spectra

Answer

To solve the question regarding the correct statement about thermal radiations emitted by a black body, we will analyze each of the given options based on our understanding of black body radiation and Planck's law.

### Step-by-Step Solution:

1. **Understanding Black Body Radiation**:
- A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It also emits radiation in a characteristic spectrum that depends only on its temperature.

2. **Analyzing Option A**:
- Option A states: "At a given temperature, the energy is distributed non-uniformly among different wavelengths."
- This is true. The spectral distribution of radiation emitted by a black body is not uniform; it varies with wavelength according to Planck's law. Therefore, this statement is correct.

3. **Analyzing Option B**:
- Option B states: "As temperature of the body increases, the energy content of all wavelengths decreases."
- This is incorrect. According to Planck's law, as the temperature of a black body increases, the total energy emitted increases, and the peak of the emission spectrum shifts to shorter wavelengths (Wien's displacement law). Thus, this statement is false.

4. **Analyzing Option C**:
- Option C states: "The product of E_lambda (spectral energy) with dλ (the spectral width) for all equal Δλ' is the same."
- This is also incorrect. The spectral energy E_lambda varies with wavelength, and thus the product E_lambda * dλ will not be the same for all wavelengths. Therefore, this statement is false.

5. **Analyzing Option D**:
- Option D states: "The thermal radiation emitted by a hot body is a discrete spectrum."
- This is incorrect. The radiation emitted by a black body is continuous across a range of wavelengths, not discrete. Hence, this statement is false.

6. **Conclusion**:
- After analyzing all options, we find that only Option A is correct. Therefore, the correct statement with respect to thermal radiation emitted by a black body is:
- **Correct Answer: Option A**.