Three stars `A, B, C` have surface temperatures `T_(A), T_(B)` and `T_(C)`. A appaears bluish, B appears reddish and C appears yellowish. We can conclude that

Options

A. `T_A gt T_C gt T_B`
B. `T_A gt T_Bgt T_C`
C. `T_B gt T_C gt T_A`
D. `T_C gt T_B gt T_A`

Answer

To solve the problem regarding the surface temperatures of the stars A, B, and C based on their colors, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Color and Wavelength Relationship**:
- The colors of the stars are given as follows:
- Star A appears bluish.
- Star B appears reddish.
- Star C appears yellowish.
- In terms of wavelength, blue light has a shorter wavelength, red light has a longer wavelength, and yellow light has a medium wavelength.

2. **Understanding Wien's Displacement Law**:
- Wien's Displacement Law states that the wavelength at which the emission of a black body spectrum is maximized (λ_max) is inversely proportional to the temperature (T) of the black body:
\[ \lambda_{max} \cdot T = b \]
where \( b \) is Wien's displacement constant.
- This implies that:
\[ \lambda_{max} \propto \frac{1}{T} \]
- Therefore, a shorter wavelength corresponds to a higher temperature.

3. **Assigning Temperatures Based on Color**:
- Since star A appears bluish (shortest wavelength), it has the highest temperature \( T_A \).
- Star C appears yellowish (medium wavelength), so it has a temperature \( T_C \) that is lower than \( T_A \) but higher than \( T_B \).
- Star B appears reddish (longest wavelength), thus it has the lowest temperature \( T_B \).

4. **Establishing the Temperature Order**:
- From the above analysis, we can conclude:
\[ T_A > T_C > T_B \]
- This means:
- \( T_A \) (blue star) is the highest.
- \( T_C \) (yellow star) is in the middle.
- \( T_B \) (red star) is the lowest.

### Conclusion:
The final conclusion we can draw is that:
\[ T_A > T_C > T_B \]