Why does a large rise of potassium outside silence neurons that a small rise excites? · Lobeworks/17

Because the same depolarisation that brings the membrane nearer threshold also inactivates sodium channels.

Why does a large rise of potassium outside silence neurons that a small rise excites?

Because the same depolarisation that brings the membrane nearer threshold also inactivates sodium channels. More potassium outside raises EK=RTFln⁡[K+]o[K+]iE_K = \frac{RT}{F}\ln\frac{[K^+]_o}{[K^+]_i}EK​=FRT​ln[K+]i​[K+]o​​ towards zero and the resting potential follows it up. A small shift puts the cell closer to threshold while most channels are still available, so it fires more easily. A large one slides far down the availability curve h∞(V)h_\infty(V)h∞​(V), leaving too few channels to make a spike at all, and the neuron falls silent in depolarisation block.