Three light sources A,B, and C emit equal amount of radiant energy per unit time. The wavelength emitted by the three sources are 450 nm, 555 nm and 700 nm respectively. The brightness sensed by an eye for the sources are `X_A, X_B and X_c` respectively. Then

Options

A. `X_AltX_B,X_CgtX_B`
B. `X_AgtX_B,X_BgtX_C`
C. `X_BgtX_A,X_CltX_B`
D. `X_BgtX_A,X_CgtX_B`

Answer

To solve the problem, we need to analyze the brightness sensed by the eye for three light sources A, B, and C, which emit equal amounts of radiant energy per unit time at different wavelengths. The wavelengths are as follows:

- Source A: 450 nm
- Source B: 555 nm
- Source C: 700 nm

The brightness sensed by the eye for these sources is represented as \(X_A\), \(X_B\), and \(X_C\).

### Step-by-Step Solution:

1. **Understand the Concept of Brightness**:
Brightness perceived by the human eye depends on the wavelength of light. The human eye is most sensitive to light around 555 nm, which corresponds to the green part of the spectrum.

2. **Identify the Maximum Brightness**:
Since source B emits light at 555 nm, it will have the highest brightness sensed by the eye, denoted as \(X_B\).

3. **Compare Wavelengths**:
- For source A (450 nm), which is in the blue region, the brightness \(X_A\) will be less than \(X_B\).
- For source C (700 nm), which is in the red region, the brightness \(X_C\) will also be less than \(X_B\).

4. **Quantify the Brightness**:
The brightness values can be estimated based on the relative sensitivity of the human eye to different wavelengths:
- \(X_B\) is the maximum brightness.
- The brightness \(X_A\) can be estimated to be lower than \(X_B\) due to the lower sensitivity at 450 nm.
- The brightness \(X_C\) can also be estimated to be lower than \(X_B\) since the eye is less sensitive to red light at 700 nm.

5. **Conclusion**:
From the analysis, we can conclude that:
\[ X_B > X_A \quad \text{and} \quad X_B > X_C \]
Therefore, the order of brightness is \(X_B > X_A > X_C\).

### Final Result:
The brightness sensed by the eye for the sources is such that \(X_B\) is the greatest, followed by \(X_A\), and then \(X_C\).