The voltmeter showed a negative reading and the sodium ion concentration remained constant outside the axon. This could be explained best by the fact that the

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The threshold for the Neuron is above the voltage reading

The negative reading on the voltmeter indicates that the inside of the axon is more negatively charged relative to the outside. This is known as the resting membrane potential.

There are two main factors that contribute to the establishment of the resting membrane potential: the selective permeability of the cell membrane to different ions and the activity of ion channels.

In the case of the axon, the sodium ion concentration remains constant outside. This means that the concentration of sodium ions in the extracellular fluid surrounding the axon is not changing. This is an important condition for maintaining the resting membrane potential.

To explain this observation, we need to consider the role of ion channels and the concentration gradient of sodium ions. The resting membrane potential of an axon is primarily influenced by two kinds of ion channels: potassium ion channels and sodium ion channels.

The potassium ion channels are more permeable to potassium ions, allowing these ions to pass through the cell membrane more easily. At rest, the potassium ion channels are mostly open, allowing potassium ions to move out of the axon. This outward movement of positively charged potassium ions contributes to the inside of the axon becoming more negatively charged relative to the outside.

On the other hand, the sodium ion channels are mostly closed at rest. This prevents the movement of sodium ions into the axon, maintaining a constant concentration of sodium ions outside the axon.

Therefore, the negative reading on the voltmeter can be best explained by the maintenance of a constant sodium ion concentration outside the axon, combined with the selective permeability of the cell membrane to potassium ions, leading to an accumulation of negative charge inside the axon.