The oxygen activity in a liquid metal can be-measured by a concentration cell using stabilised zirconia electrolyte PO₂⁽¹⁾ | ZrO₂ based solid electrolyte | PO₂⁽²⁾
Where, PO₂⁽¹⁾ is the reference oxygen pressure and PO₂⁽²⁾ is the oxygen pressure in equilibrium with liquid metal. If, F is Faraday constant, the EMF of the cell is equal to

A. $$ - \frac{{RT}}{{2F}}.\frac{{PO_2^{\left( 2 \right)}}}{{PO_2^{\left( 1 \right)}}}$$

B. $$ - \frac{{RT}}{{4F}}.\frac{{PO_2^{\left( 2 \right)}}}{{PO_2^{\left( 1 \right)}}}$$

C. $$ - \frac{{RT}}{{2F}}In\frac{{PO_2^{\left( 2 \right)}}}{{PO_2^{\left( 1 \right)}}}$$

D. $$ - \frac{{RT}}{{4F}}In\frac{{PO_2^{\left( 2 \right)}}}{{PO_2^{\left( 1 \right)}}}$$

Answer: Option D