Resistance of 0.2 M solution of an electrolyte is 50 Ω. The specific conductance of the solution is 1.4 S m⁻¹. The resistance of 0.5 M solution of the same electrolyte is 280 Ω. The molar conductivity of 0.5 M solution of the electrolyte in S m² mol⁻¹ is:

We know, R = 1/κ × l/A
where R is resistance, κ is specific conductance, l is length and A is area of cross section.
For 0.2 M solution,
R = 50 Ω, κ = 1.4 S m⁻¹
κ = 1/R × l/A = 1.4 S m⁻¹
For 0.5 M solution,
R = 280 Ω
κ = 1/280 × l/A
Since l/A is constant,
1.4 = 1/50 × l/A
l/A = 1.4 × 50 = 70 m⁻¹
κ for 0.5 M solution = 1/280 × 70 = 0.25 S m⁻¹
Molar conductivity (Λm) = κ/M
where M is molar concentration.
Λm = 0.25 S m⁻¹ / 0.5 mol m⁻³ = 0.5 S m² mol⁻¹ = 5 × 10⁻¹ S m² mol⁻¹
Λm = 5 × 10² × 10⁻³ S m² mol⁻¹ = 5 × 10⁻¹ S m² mol⁻¹
The correct option is 5 × 10²