Three stars A, B and C appears as green, red and blue respectively. The star having minimum temperature is

Options

A. A
B. B
C. C
D. A and B, have the same temperature

Answer

To determine which star among A, B, and C has the minimum temperature based on their colors (green, red, and blue), we can use Wien's Law. Here is a step-by-step solution:

### Step 1: Understand Wien's Law
Wien's Law states that the wavelength at which the emission of a black body spectrum is maximized (λ_max) is inversely proportional to its absolute temperature (T). This can be mathematically expressed as:
\[ \lambda_{max} \cdot T = b \]
where \( b \) is Wien's constant (approximately \( 2.898 \times 10^{-3} \, \text{m} \cdot \text{K} \)).

### Step 2: Identify the Colors and Their Corresponding Wavelengths
The colors of the stars are:
- Star A: Green
- Star B: Red
- Star C: Blue

In the electromagnetic spectrum, the order of increasing wavelength is:
- Blue (shortest wavelength)
- Green (medium wavelength)
- Red (longest wavelength)

### Step 3: Relate Wavelength to Temperature
According to Wien's Law, since temperature is inversely proportional to wavelength:
- The star with the shortest wavelength (Blue) has the highest temperature.
- The star with the medium wavelength (Green) has a medium temperature.
- The star with the longest wavelength (Red) has the lowest temperature.

### Step 4: Conclusion
From the analysis, we can conclude that:
- Star C (Blue) has the highest temperature.
- Star A (Green) has a medium temperature.
- Star B (Red) has the lowest temperature.

Thus, the star with the minimum temperature is **Star B (Red)**.

### Summary of the Solution
The star having the minimum temperature is the one that appears red (Star B).

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