In a resting cell, if potassium ion channels open and allow potassium to diffuse freely across the membrane, what will be the result?

a. no change in membrane potential will occur
b. hyperpolarization will occur
c. a depolarization will occur
d. a repolarization will occur

b. hyperpolarization will occur

The correct answer is b. hyperpolarization will occur.

When potassium ion channels open, potassium ions will move out of the cell due to the concentration gradient. Since potassium ions are positively charged, the movement of these ions out of the cell will result in an increased negative charge inside the cell, making the cell more negative or hyperpolarized. This hyperpolarization will further increase the resting membrane potential, making it more difficult for the cell to generate an action potential.

If potassium ion channels open and allow potassium to diffuse freely across the membrane of a resting cell, it will result in a change in the membrane potential. To understand the specific outcome, we need to consider the direction in which potassium ions flow.

In a resting cell, the concentration of potassium ions is higher inside the cell compared to the outside. This concentration gradient creates a tendency for potassium ions to move out of the cell. However, the resting cell's membrane also has a negative charge inside with respect to the outside. This electrical gradient attracts potassium ions into the cell.

When potassium channels open, potassium ions can move freely across the membrane, driven by both the concentration and electrical gradients. Since the concentration gradient for potassium ions is higher outside the cell, they will tend to move out. As a result, positive charge is leaving the cell and negative charge is staying inside. This movement of positive charge out of the cell leads to a change in the membrane potential.

Given these factors, the correct answer to the question is:

b. Hyperpolarization will occur.

Hyperpolarization refers to an increase in the negative charge inside the cell, making it more negative than the resting membrane potential. This is caused by the efflux of positively charged potassium ions, which brings the membrane potential further away from the threshold required to trigger an action potential.

In summary, opening of potassium ion channels in a resting cell will result in the efflux of potassium ions, causing hyperpolarization of the cell membrane.