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(B) Step $1$: Calculate the cell constant $(G^* = l/a)$.Given for $0.1 \, M$ solution: $R = 100 \, \Omega$ and $\kappa = 1.29 \, S \, m^{-1}$.$G^* = \

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$12.4$

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(B) Step $1$: Calculate the cell constant $(G^* = l/a)$.Given for $0.1 \, M$ solution: $R = 100 \, \Omega$ and $\kappa = 1.29 \, S \, m^{-1}$.$G^* = \kappa 	imes R = 1.29 \, S \, m^{-1} 	imes 100 \, \Omega = 129 \, m^{-1}$.Step $2$: Calculate conductivity $(\kappa)$ for $0.2 \, M$ solution.Given $R = 520 \, \Omega$ for $0.2 \, M$ solution.$\kappa = \frac{G^*}{R} = \frac{129 \, m^{-1}}{520 \, \Omega} \approx 0.248 \, S \, m^{-1}$.Step $3$: Calculate molar conductivity $(\Lambda_m)$.$\Lambda_m = \frac{\kappa}{C} = \frac{0.248 \, S \, m^{-1}}{0.2 \, mol \, L^{-1}} = \frac{0.248 \, S \, m^{-1}}{0.2 	imes 10^3 \, mol \, m^{-3}} = 1.24 	imes 10^{-3} \, S \, m^2 \, mol^{-1}$.Converting to the required units $(	imes 10^{-4} \, S \, m^2 \, mol^{-1})$:$1.24 	imes 10^{-3} = 12.4 	imes 10^{-4} \, S \, m^2 \, mol^{-1}$.

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