Resistance of a conductivity cell filled with 0.1 M KCl is 100 ohm. If the resistence of the same cell when filled with 0.02 M KCl solution is 520 ohms, calculate the conductivity and molar conductivity of 0.02 M KCl solution. Conductivity of 0.1 KCl solution is `1.29xx10^(-2)" ohm "^(-1)cm^(-1)`.

Explanation

To solve the problem, we need to calculate the conductivity and molar conductivity of a 0.02 M KCl solution using the given data about the resistance of the conductivity cell filled with different concentrations of KCl.

### Step-by-Step Solution:

1. **Identify Given Data:**
- Resistance of 0.1 M KCl solution, \( R_1 = 100 \, \Omega \)
- Resistance of 0.02 M KCl solution, \( R_2 = 520 \, \Omega \)
- Conductivity of 0.1 M KCl solution, \( \kappa_1 = 1.29 \times 10^{-2} \, \Omega^{-1} \text{cm}^{-1} \)
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