For a general electrochemical reaction of the type:

$aA+bB\overset{ne^-}{\longrightarrow}cC+dD$ Nernst equation can be written as:

$E_{cell}=E_{cell}^º-\frac{RT}{nF}ln\frac{[C]^c[D]^d}{[A]^a[B]^b}$

The correct answer is Option (3) → $E_{cell}=E_{cell}^º-\frac{RT}{nF}ln\frac{[C]^c[D]^d}{[A]^a[B]^b}$

The Nernst equation is used to relate the cell potential of an electrochemical cell to the concentrations (or activities) of the species involved in the reaction. For the general electrochemical reaction:

\(aA + bB \longrightarrow cC + dD\)

The Nernst equation is given by:

\(E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln \left( \frac{[C]^c [D]^d}{[A]^a [B]^b} \right)\)

Where:

\( E_{\text{cell}} \) is the cell potential at non-standard conditions.

\( E^\circ_{\text{cell}} \) is the standard cell potential (when all reactants and products are at 1 M concentration or 1 atm pressure).

\( R \) is the gas constant (\(8.314 \, \text{J mol}^{-1} \text{K}^{-1}\)).

\( T \) is the temperature in Kelvin.

\( n \) is the number of electrons transferred in the reaction.

\( F \) is the Faraday constant (\(96,485 \, \text{C mol}^{-1}\)).

\( [A], [B], [C], [D] \) are the concentrations of the species A, B, C, and D, respectively.

\( a, b, c, d \) are the stoichiometric coefficients of the species in the balanced chemical equation.

Therefore, the correct Nernst equation is:

\(E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{RT}{nF} \ln \left( \frac{[C]^c [D]^d}{[A]^a [B]^b} \right)\)

This matches option 3.