The electrical potential difference necessary for a single ion to be at equilibrium across a membrane is best described by the (NOT RELATED)
## Core Concept
The **Nernst equation** is used to calculate the equilibrium potential (also referred to as the Nernst potential) for an ion. This equation takes into account the concentration gradient of the ion across a membrane and the charge of the ion. The electrical potential difference necessary for a single ion to be at equilibrium across a membrane is essentially the equilibrium potential for that ion.
## 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. This equation precisely describes the electrical potential difference at which the chemical and electrical gradients for a specific ion are equal, and there is no net movement of the ion across the membrane.
## Why Each Wrong Option is Incorrect
- **Option A:** This option is incorrect because it does not correspond to any recognized equation related to the description provided.
- **Option B:** This option is incorrect because, although it might resemble a form of an equation, it does not accurately represent the Nernst equation or any other relevant equation that describes the equilibrium potential for an ion.
- **Option C:** This option, **the Goldman-Hodgkin-Katz equation**, while relevant to calculating the resting membrane potential by taking into account the concentrations of multiple ions, does not specifically describe the equilibrium potential for a single ion.
## Clinical Pearl / High-Yield Fact
A key point to remember is that the **Nernst equation** can be simplified at human body temperature (37°C) to (E_{ion} = frac{61.54}{z} logleft(frac{[ion]_{outside}}{[ion]_{inside}}right)) for ease of calculation. This equation is fundamental in understanding how ions move across cell membranes and is crucial for understanding neuronal and muscle physiology.
## Correct Answer: .