No, this is because the transport of K and Na ion across the plasma membrane require active transport and this require ATP.
The cell membrane
A membrane that lets some substances pass through but not others is known as a semipermeable membrane. Other terms that describe this type of membrane are: selectively permeable, partially permeable, or differentially permeable.
A cell membrane is found on both plant and animal cells it selectively chooses what substances may enter or leave the cell. Hence the term selectively permeable. For a more advanced explanation I recommend you research protein icebergs and the different types of transport a membrane can take part in. Example active transport
Semi permeable membrane means a very thin layer of material which allows some molecule to pass through them and prevent some molecule to pass through them. Osmosis is the passage of water from a dilute solution via a membrane which is semi permeable to a more concentrate solution. So the membrane should be semi-permeable so as to only allow the movement of H2O molecules and not the other molecules of the mixture.
selective permabiltiy
Even when both those atoms are encapsulated with water, potassium is smaller than sodium.
The cell membrane
A membrane that lets some substances pass through but not others is known as a semipermeable membrane. Other terms that describe this type of membrane are: selectively permeable, partially permeable, or differentially permeable.
During an action potential the neuron receives a stimulus causing the cell membrane to become more permeable to sodium than potassium, calling the polarity to change.
It will cause it to become rigid
Some substances, including sodium and potassium, use a process called active transport to permeate cell walls. Active transport is controlled by other body systems. It limits the quantity of these substances passing through the plasma membrane to match the needs of the body.
The effect of heat on beetroot is that the membrane becomes impacted. It causes the membrane to be more permeable.
Potassium and Sodium
When a neuron is resting then inside of the cell membrane is more negative than outside.
If the membrane is not permeable to either sodium and chloride ions or water then the concentrations of the liquids would remain the same. However, if the membrane was permeable to water or the ions then the plain water would become more salty while the salty water would become more dilute (due diffusion/osmosis, depending on the membrane's permeability).
the cholesterol will help to prevent the fatty-acid tails of the phospholipids bilayer from sticking together, which contributes to the fluidity of the plasma membrane.
A cell membrane is found on both plant and animal cells it selectively chooses what substances may enter or leave the cell. Hence the term selectively permeable. For a more advanced explanation I recommend you research protein icebergs and the different types of transport a membrane can take part in. Example active transport