## **Core Concept**
The equilibrium potential for an ion, also known as the Nernst potential, is the membrane potential at which the electrical and chemical gradients for a specific ion are balanced. This concept is fundamental to understanding how ions move across cell membranes and how neurons and muscle cells generate action potentials. The equilibrium potential is calculated using the Nernst equation.

## **Why the Correct Answer is Right**
The Nernst equation is given by (E_{ion} = frac{RT}{zF} lnleft(frac{[ion]_{outside}}{[ion]_{inside}}right)), where (E_{ion}) is the equilibrium potential for the ion, (R) is the ideal gas constant, (T) is the temperature in Kelvin, (z) is the charge of the ion, (F) is Faraday's constant, and ([ion]_{outside}) and ([ion]_{inside}) are the concentrations of the ion outside and inside the cell, respectively. At room temperature (20°C or 293K), (frac{RT}{F}) is approximately 25.85 mV, which can be rounded to 61 mV at body temperature (37°C or 310K) for simplicity. The equation can thus be simplified to (E_{ion} = frac{61}{z} logleft(frac{[ion]_{outside}}{[ion]_{inside}}right)) or in natural logarithm form (E_{ion} = frac{61}{z} lnleft(frac{[ion]_{outside}}{[ion]_{inside}}right)) when using base (e). This matches option , making it the correct formula for calculating the equilibrium potential.

## **Why Each Wrong Option is Incorrect**
- **Option A:** This option does not match the Nernst equation. It seems to lack the proper formulation and does not correctly represent how the equilibrium potential is calculated.
- **Option B:** This option might seem similar but does not accurately represent the Nernst equation, particularly with the use of "log" without specifying the base and not accurately reflecting the relationship between the concentrations and the ion's charge.
- **Option D:** This option does not correctly represent the Nernst equation. The formulation seems incorrect, and it does not properly account for the charge of the ion or the concentration gradient.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the equilibrium potential for an ion helps predict the direction in which the ion will move across the membrane. For example, the equilibrium potential for sodium ((E_{Na})) is typically around +60 mV, and for potassium ((E_K)), it's around -90 mV. This knowledge is crucial for understanding action potential generation in neurons and muscle cells.

## **Correct Answer:** .