## **Core Concept**
The equilibrium potential for an ion is the membrane potential at which the electrical and chemical gradients for that ion are equal, resulting in no net movement of the ion across the membrane. This concept is based on the Nernst equation, which calculates the equilibrium potential for a specific ion. The equilibrium potential for potassium (K+) is crucial in understanding the resting membrane potential and the repolarization phase of the action potential.

## **Why the Correct Answer is Right**
The Nernst equation for an ion at human body temperature (approximately 37°C) can be simplified to: (E_{ion} = frac{61.54}{z} logleft(frac{[ion]_{outside}}{[ion]_{inside}}right)), where (z) is the charge of the ion, and ([ion]_{outside}) and ([ion]_{inside}) are the concentrations of the ion outside and inside the cell, respectively. For potassium (K+), (z = +1), ([K^+]_{outside} approx 5) mM, and ([K^+]_{inside} approx 150) mM. Substituting these values into the Nernst equation yields: (E_{K+} = 61.54 logleft(frac{5}{150}right) = 61.54 logleft(frac{1}{30}right) = 61.54 times -1.477 = -88.46) mV, which is approximately (-90) mV. This matches option .

## **Why Each Wrong Option is Incorrect**
- **Option A:** This value does not match the calculated equilibrium potential for K+ using the Nernst equation.
- **Option B:** This value seems too positive for the equilibrium potential of K+, given that K+ tends to leave the cell, making the inside more negative relative to the outside.
- **Option D:** This option is far too positive and does not align with the calculated value or the physiological understanding of K+ equilibrium potential.

## **Clinical Pearl / High-Yield Fact**
A key point to remember is that the resting membrane potential of most neurons is close to the equilibrium potential for K+, around (-70) to (-80) mV, but not exactly equal due to the influence of other ions, especially sodium. The equilibrium potential for K+ helps explain why the membrane potential hyperpolarizes (becomes more negative) during increased K+ permeability.

## **Correct Answer:** . -90 mV