Which of the following curve represents the variation of `lambda_(M)` with `sqrt(C)` for `AgNO_(3)`?

Options

A.
B.
C.
D.

Explanation

To determine the variation of \(\lambda_m\) with \(\sqrt{C}\) for \(AgNO_3\), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The relationship given is:
\[ \lambda_m = \lambda_{m0} - B \sqrt{C} \]
where \(\lambda_m\) is the molar conductivity, \(\lambda_{m0}\) is the molar conductivity at infinite dilution, \(B\) is a constant, and \(C\) is the concentration.

2. **Rearranging the Equation**: We can rearrange the equation to express it in a linear form:
\[ \lambda_m = \lambda_{m0} - B \sqrt{C} \]
This can be rewritten as:
\[ \lambda_m = -B \sqrt{C} + \lambda_{m0} \]
This is in the form of \(y = mx + c\), where:
- \(y\) is \(\lambda_m\)
- \(x\) is \(\sqrt{C}\)
- \(m\) (slope) is \(-B\)
- \(c\) (y-intercept) is \(\lambda_{m0}\)

3. **Identify the Characteristics of the Graph**:
- The slope \(m = -B\) indicates that the slope is negative.
- The y-intercept is \(\lambda_{m0}\), which is the value of \(\lambda_m\) when \(\sqrt{C} = 0\).

4. **Plotting the Graph**:
- On the graph, plot \(\lambda_m\) on the y-axis and \(\sqrt{C}\) on the x-axis.
- Since the slope is negative, the line will slope downwards from left to right.
- The line will start at \(\lambda_{m0}\) on the y-axis when \(\sqrt{C} = 0\).

5. **Conclusion**: The graph will show a straight line that decreases as \(\sqrt{C}\) increases, confirming that \(\lambda_m\) decreases with increasing concentration.

### Final Answer:
The correct curve that represents the variation of \(\lambda_m\) with \(\sqrt{C}\) for \(AgNO_3\) is a straight line with a negative slope starting from \(\lambda_{m0}\).