$R=50 \Omega$

$\kappa=1.45 S m^{-1}=1.4 \times 10^{-2} S \mathrm{cm}^{-1}$

Now, $R=\rho {\frac{\ell}{a}}=\frac{1}{\kappa} \times \frac{\ell}{a}$

$\Rightarrow \frac{\ell}{a}=R \times \kappa=50 \times 1.4 \times 10^{-2}$

For $0.5 M$ solution

$R=280 \Omega ; \kappa=?$

$\frac{\ell}{a}=50 \times 1.4 \times 10^{-2}$

$\Rightarrow R=\rho \frac{\ell}{a}=\frac{1}{\kappa} \times \frac{\ell}{a}$

$\Rightarrow \quad \kappa=\frac{1}{280} \times 50 \times 1.4 \times 10^{-2}$

$=\frac{1}{280} \times 70 \times 10^{-2}=2.5 \times 10^{-3} S c m^{-1}$

Now, $\Lambda_{m}=\frac{\kappa \times 1000}{M}=\frac{2.5 \times 10^{-3} \times 1000}{0.5}$

$=5 S c m^{2} m o l^{-1}=5 \times 10^{-4} S m^{2} m o l^{-1}$