On observing light from three different stars `P`, `Q` and `R`, it was found that intensity of violet colour is maximum in the spectrum of `P`, the intensity of green colour is maximum in the spectrum of `R` and the intensity of red colour is maximum in the spectrum of `Q`. if `T_(P)`, `T_(Q)` and `T_(R)` are respective absolute temperature of `P`, `Q` and `R`. then it can be concluded from the above observation that

Options

A. `T_(p) gt T_(Q) gt T_(R)`
B. `T_(P) gt T_(R) gt T_(Q)`
C. `T_(P) lt T_(R) lt T_(Q)`
D. `T_(P) lt T_(Q) lt T_(R)`

Answer

To solve the problem, we need to analyze the relationship between the colors observed in the spectra of stars P, Q, and R and their respective absolute temperatures. We will use Wien's Displacement Law, which states that the wavelength at which the intensity of radiation is maximum (λm) is inversely proportional to the absolute temperature (T) of the black body.

### Step-by-Step Solution:

1. **Understanding Wien's Displacement Law**:
According to Wien's Displacement Law, the maximum wavelength (λm) of radiation emitted by a black body is given by:
\[ \lambda_m \propto \frac{1}{T} \]
This implies that:
\[ \lambda_m = \frac{B}{T} \]
where B is a constant.

2. **Identifying the Colors and Their Wavelengths**:
From the problem, we know:
- Star P has maximum intensity in violet light.
- Star Q has maximum intensity in red light.
- Star R has maximum intensity in green light.

The order of wavelengths from longest to shortest is:
\[ \lambda_{red} > \lambda_{green} > \lambda_{violet} \]

3. **Relating Wavelengths to Temperatures**:
Since the maximum wavelength is inversely proportional to temperature, we can conclude:
- For star P (violet), which has the shortest wavelength, the temperature \( T_P \) will be the highest.
- For star R (green), which has a medium wavelength, the temperature \( T_R \) will be in the middle.
- For star Q (red), which has the longest wavelength, the temperature \( T_Q \) will be the lowest.

4. **Establishing the Relationship**:
From our observations:
\[ T_P > T_R > T_Q \]

5. **Conclusion**:
Therefore, the final relationship between the temperatures of the stars is:
\[ T_P > T_R > T_Q \]

### Final Answer:
The conclusion from the observations is:
\[ T_P > T_R > T_Q \]