This page assumes you know nothing. We build every symbol the parent note Biological Importance of Na, K, Ca, Mg throws at you, one brick at a time. Never move on until the picture makes sense.
The raised sign is called the superscript charge. So:
Na+ means a sodium atom that lost one electron → charge +1.
Mg2+ means a magnesium atom that lost two electrons → charge +2.
Cl− (chloride) has one extra electron → charge −1.
PO43− (phosphate) has three extra negatives → charge −3.
The little number before the + or − is how many units of charge. No number written = one.
Figure s01 (below): read it left→right. On the left is a neutral atom — count the black electron dots, they balance the + nucleus. The red dot is the electron escaping. On the right, the same atom is now short one electron, so it carries a leftover +1 — it has become an ion. This picture is the definition of "ion" in one glance.
Because every ion has its own leftover charge, we need one letter that stands for "whatever that charge is" — so a single formula can serve Na⁺, Cl⁻, Mg²⁺ and all the rest. That letter is z:
Before we talk about crowdedness we need a way to count particles. Ions are unimaginably tiny — a spoon of salt holds more of them than there are stars in the sky. So chemists count them in giant fixed bundles.
Think of a swimming pool. If you drop 10 sugar cubes into a small cup, it is very sweet. Drop the same 10 cubes into a giant pool — barely sweet. What matters is how crowded the particles are, not how many total.
Figure s02 (below): the black wall is the cell membrane. The left side is packed with black dots (high [X]), the right side is nearly empty (low [X]). The red arrow is the stored push — the direction crowded particles want to move, held back only by the sealed wall. That red arrow is what "a gradient stores energy" means.
Now, ions carry charge. If more positive charge piles up on one side of the wall than the other, that side is electrically "higher." That electrical difference is called voltage.
Figure s03 (below): the wall again. The top shows extra + outside and extra − inside — that lopsided charge is the voltage E. The black arrow is the concentration push (crowded → empty); the red arrow is the electrical push pointing the opposite way. When the red arrow exactly balances the black arrow, no ion flows on average — that balance is what the Nernst equation computes.
We are about to meet the parent's boxed formula, but it hides four things you have not seen yet: the letters R, T, F and the function ln. Let us earn each one before it appears.
Now the function. When we combine the two pushes we will need to turn a ratio of crowdings into an amount of energy — and the tool for that is the logarithm.
Read this as a story in three streams that meet at the Nernst equation, following the arrows top to bottom:
Stream 1 (charge): an atom loses/gains electrons → becomes an ion with charge z → the size of z splits our metals into mobile (+1) and sticky (+2).
Stream 2 (crowding): we count particles in moles → crowdedness is written [X] → an unequal crowd stores energy (a gradient).
Stream 3 (electricity): charged ions across a sealed wall pile up → this is the voltage E.
They meet: the concentration push (Stream 2) and the electrical push (Stream 3) balance → the Nernst equation ties them, giving the resting potential.
Figure s04 (below) draws exactly this: three columns of black boxes flowing downward into one red box — the Nernst equation — where the two pushes balance.
Test yourself — cover the right side and answer out loud.
What does the raised + or 2+ after a symbol mean?
The leftover charge on an ion (electrons lost); the number is how many charge units.
What does the letter z stand for, and can it be negative?
The charge number of an ion, with sign (+1 Na⁺/K⁺, +2 Mg²⁺/Ca²⁺, −1 for the anion Cl⁻).
What is a "mole" in one phrase?
A counting word for a fixed huge bundle of particles (about 6×1023), like "a dozen" means 12.
What does [X]out mean in words?
The concentration (crowdedness) of substance X on the outside of the cell.
Why does a concentration difference store energy?
Crowded particles push toward emptier space, like water held behind a dam; releasing them releases energy.
What is a membrane and why does it matter?
The sealed oily cell wall; being sealed lets inside and outside hold different concentrations.
Voltage is measured in volts — what does one volt physically mean?
One joule of energy per one coulomb of charge (1V=1J/C); that is why volts measure a "push."
What does E=−70mV tell you?
The inside of the cell is electrically more negative than the outside by 70 millivolts.
What are the two pushes an ion feels across the membrane?
The concentration push (down the gradient) and the electrical push (from voltage).
What are R, T, F in one phrase each?
T = how warm (jiggle); R = fixed exchange rate turning warmth into energy per mole; F = fixed exchange rate turning charge into voltage units.
Why does ln appear in the Nernst equation?
Equal doublings of the crowding gap add equal chunks of push; the function with that property is the logarithm — it turns multiplying ratios into adding energy.
How does the sign of z change the result for an anion like Cl⁻?
A negative z flips the voltage: the same crowding ratio gives a potential leaning the opposite way to a cation.
What is a pump, and what fuel does it use?
A protein that moves ions uphill against their gradient, paying with ATP (see ATP and Bioenergetics).
