If x is specific resistance of the electrolyte solution and y is the molarity of the solution, rthen `^^_(m)` is given by:

Options

A. `(1000x)/(y)`
B. `1000(y)/(x)`
C. `(1000)/(xy)`
D. `(xy)/(1000)`

Explanation

To solve the problem, we need to derive the expression for molar conductivity (λ_m) in terms of specific resistance (X) and molarity (Y) of the electrolyte solution.

### Step-by-Step Solution:

1. **Understand the Definitions**:
- Specific resistance (X) is also known as resistivity. It is a measure of how strongly a material opposes the flow of electric current.
- Molarity (Y) is the concentration of a solution expressed as the number of moles of solute per liter of solution.

2. **Identify the Formula for Molar Conductivity**:
- The formula for molar conductivity (λ_m) is given by:
\[ \lambda_m = \frac{\kappa \times 1000}{Y} \]
where κ (kappa) is the conductivity of the solution.

3. **Relate Conductivity to Specific Resistance**:
- Conductivity (κ) is the reciprocal of specific resistance (X):
\[ \kappa = \frac{1}{X} \]

4. **Substitute Conductivity into the Molar Conductivity Formula**:
- Substitute the expression for conductivity into the molar conductivity formula:
\[ \lambda_m = \frac{\frac{1}{X} \times 1000}{Y} \]

5. **Simplify the Expression**:
- This simplifies to:
\[ \lambda_m = \frac{1000}{XY} \]

6. **Final Expression**:
- Thus, the expression for molar conductivity (λ_m) in terms of specific resistance (X) and molarity (Y) is:
\[ \lambda_m = \frac{1000}{XY} \]

### Conclusion:
The final answer is:
\[ \lambda_m = \frac{1000}{XY} \]