Shown below are the black body radiation curves at temperature `T_(1)` and `T_(2) (T_(2) gt T_(1))`. Which of the following plots is correct?

Options

A.
B.
C.
D.

Explanation

To solve the problem regarding black body radiation curves at different temperatures \( T_1 \) and \( T_2 \) (where \( T_2 > T_1 \)), we can follow these steps:

### Step 1: Understand Wien's Displacement Law
Wien's Displacement Law states that the wavelength \( \lambda_m \) at which the intensity of radiation is maximum is inversely proportional to the temperature \( T \) of the black body. Mathematically, it is expressed as:
\[ \lambda_m T = b \]
where \( b \) is a constant.

### Step 2: Relate the Wavelengths to the Temperatures
From the law, we can derive that:
\[ \lambda_{m1} T_1 = \lambda_{m2} T_2 \]
Since \( T_2 > T_1 \), it follows that:
\[ \lambda_{m2} < \lambda_{m1} \]
This means that the wavelength of maximum intensity for the higher temperature \( T_2 \) (denoted as \( \lambda_{m2} \)) is shorter than that for the lower temperature \( T_1 \) (denoted as \( \lambda_{m1} \)).

### Step 3: Analyze the Black Body Radiation Curves
The black body radiation curves show intensity versus wavelength. For the two temperatures:
- The curve for \( T_2 \) will peak at a shorter wavelength than the curve for \( T_1 \).
- The intensity of radiation at all wavelengths will be higher for \( T_2 \) compared to \( T_1 \).

### Step 4: Identify the Correct Plot
When looking at the plots:
- The plot that shows the curve for \( T_2 \) peaking at a shorter wavelength than the curve for \( T_1 \) is the correct one.
- The maximum intensity for \( T_2 \) should be higher than that for \( T_1 \) at the corresponding wavelengths.

### Conclusion
Based on the analysis, the correct plot will be the one where:
- The curve for \( T_2 \) is to the left of the curve for \( T_1 \) on the wavelength axis, indicating that \( \lambda_{m2} < \lambda_{m1} \).