Resistance of a conductivity cell filled with a solution of an electrolyte of concentration$0.1M$ is $100ohm$. The conductivity of this solution is $1.29S{m}^{-1}$. Resistance of the same cell when filled with $0.2M$ of the same solution is $520ohm$. The molar conductivity of $0.2M$ solution of the electrolyte will be:

The correct option is A

$124\times {10}^{-5}S{m}^{2}mo{l}^{-1}$

Cell constant is same for a particular cell. It is a constant.

We know,
$\text{Conductivity,}\kappa =\frac{1}{R}\times \text{Cell constant}$
For $0.1M$ solution,

$\text{Resistance,}\left(R\right)=100\Omega$
$\text{Conductivity,}\kappa =1.29S{m}^{-1}$

$\kappa =\frac{1}{R}\times \frac{l}{A}$

$1.29=\frac{1}{100}\times \frac{l}{A}$

$\text{Cell constant,}\frac{l}{A}=129m^{-1}$

For $0.2M$ solution,
$\text{Resistance,}\left(R\right)=520\Omega$
$\text{Conductivity,}\kappa =\frac{1}{R}\times \text{Cell constant}$
$\text{Conductivity,}\kappa =\frac{1}{520}\times 129$
$\text{Conductivity,}\kappa =0.248S{m}^{-1}$

${\Lambda }_m=\frac{\kappa }{C}$
Also, we know
$1L={10}^{-3}{m}^3$
$1L^{-1}={10}^3{m}^{-3}$
$\text{Molar concentration,}\left(C\right)=0.2\times {10}^{3}mol{m}^{-3}$
${\Lambda }_m=\frac{0.248}{0.2\times {10}^3}$

${\Lambda }_m=124\times {10}^{-5}S{m}^{2}mo{l}^{-1}$