A black body radiates heat at temperatures `'T_1'` and `'T_2'` `(T_2 gt T_1)` The frequency corresponding to maximum energy is

Options

A. More at `T_1`
B. More at `T_2`
C. Equal for `T_1` and `T_2`
D. Independent of `T_1` and `T_2`

Explanation

To solve the problem regarding the frequency corresponding to maximum energy radiated by a black body at two different temperatures \(T_1\) and \(T_2\) (where \(T_2 > T_1\)), we can follow these steps:

### Step-by-Step Solution

1. **Understanding Black Body Radiation**: A black body is an idealized physical object that absorbs all incident electromagnetic radiation. According to Planck's law, the energy radiated by a black body is dependent on its temperature.

2. **Wien's Displacement Law**: This law states that the wavelength (\(\lambda\)) at which the emission of radiation is maximized is inversely proportional to the temperature (\(T\)) of the black body. Mathematically, it can be expressed as:
\[ \lambda_{\text{max}} = \frac{b}{T} \]
where \(b\) is Wien's displacement constant.

3. **Applying Wien's Law**: For two temperatures \(T_1\) and \(T_2\) (with \(T_2 > T_1\)):
- The wavelength corresponding to maximum energy at temperature \(T_1\) is:
\[ \lambda_1 = \frac{b}{T_1} \]
- The wavelength corresponding to maximum energy at temperature \(T_2\) is:
\[ \lambda_2 = \frac{b}{T_2} \]

4. **Comparing Wavelengths**: Since \(T_2 > T_1\), it follows that:
\[ \lambda_2 < \lambda_1 \]
This means that the wavelength at which maximum energy is radiated decreases as the temperature increases.

5. **Relating Wavelength to Frequency**: The relationship between wavelength (\(\lambda\)) and frequency (\(f\)) is given by the equation:
\[ c = \lambda f \]
where \(c\) is the speed of light. Rearranging this gives:
\[ f = \frac{c}{\lambda} \]

6. **Finding Frequencies**: Since \(\lambda_2 < \lambda_1\), we can conclude:
\[ f_2 = \frac{c}{\lambda_2} > f_1 = \frac{c}{\lambda_1} \]
This indicates that the frequency corresponding to maximum energy at temperature \(T_2\) is greater than that at temperature \(T_1\).

7. **Conclusion**: Therefore, the frequency corresponding to maximum energy is higher at the higher temperature \(T_2\).

### Final Answer
The frequency corresponding to maximum energy is greater at temperature \(T_2\) than at temperature \(T_1\).