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Shown below are the black body radiation...

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?

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To solve the problem regarding the black body radiation curves at temperatures \( T_1 \) and \( T_2 \) (where \( T_2 > T_1 \)), we will use Wien's Displacement Law and the characteristics of black body radiation. ### Step-by-Step Solution: 1. **Understand Black Body Radiation**: Black body radiation refers to the electromagnetic radiation emitted by a perfect black body in thermal equilibrium. The intensity of radiation emitted varies with wavelength and temperature. 2. **Apply Wien's Displacement Law**: According to Wien's Displacement Law, the wavelength \( \lambda_m \) at which the intensity of radiation is maximum for a black body is inversely proportional to the temperature \( T \): \[ \lambda_m T = b \] where \( b \) is a constant (Wien's displacement constant). 3. **Analyze the Given Temperatures**: Since \( T_2 > T_1 \), it follows from Wien's Law that: \[ \lambda_{m2} T_2 = \lambda_{m1} T_1 \] This implies that \( \lambda_{m2} < \lambda_{m1} \) because \( T_2 > T_1 \). Therefore, the peak wavelength for the higher temperature \( T_2 \) will be shorter than that for the lower temperature \( T_1 \). 4. **Interpret the Curves**: In the black body radiation curves: - The curve for \( T_1 \) will peak at a longer wavelength (larger \( \lambda_{m1} \)). - The curve for \( T_2 \) will peak at a shorter wavelength (smaller \( \lambda_{m2} \)). 5. **Identify the Correct Plot**: Among the given options, the correct plot will show: - The curve corresponding to \( T_2 \) shifted to the left (indicating a shorter peak wavelength) compared to the curve for \( T_1 \). 6. **Conclusion**: Based on the analysis, the correct plot that represents the black body radiation curves at temperatures \( T_1 \) and \( T_2 \) (with \( T_2 > T_1 \)) is the one where the curve for \( T_2 \) is to the left of the curve for \( T_1 \).
To solve the problem regarding the black body radiation curves at temperatures \( T_1 \) and \( T_2 \) (where \( T_2 > T_1 \)), we will use Wien's Displacement Law and the characteristics of black body radiation. ### Step-by-Step Solution: 1. **Understand Black Body Radiation**: Black body radiation refers to the electromagnetic radiation emitted by a perfect black body in thermal equilibrium. The intensity of radiation emitted varies with wavelength and temperature. 2. **Apply Wien's Displacement Law**: According to Wien's Displacement Law, the wavelength \( \lambda_m \) at which the intensity of radiation is maximum for a black body is inversely proportional to the temperature \( T \): \[ ...
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