I was recently asked to comment on this very interesting podcast (49 minutes) on The Electron, hosted by Melvyn Bagg on In Our Time.
https://www.bbc.co.uk/sounds/play/m001cf1n

This led me to the Dirac wave equation article on Wikipedia.
https://en.wikipedia.org/wiki/Dirac_equation

To any seasoned mathematician, physicist or scientist there is certainly enough there to make your head spin (pun intended).

 

The Electron seems very good for the most part but:
The first thing he says @ 1:15 is that when charge our laptop or car we store electrons. I'm sure he knows better than to say that to a scientific audience.
A fully charged battery and a fully discharged battery contain exactly the same number of electrons. The difference is energy stored by the chemical manipulation (charge separation) of those internal charges.

 

The Electron seems very good for the most part but:
The first thing he says @ 1:15 is that when charge our laptop or car we store electrons. I'm sure he knows better than to say that to a scientific audience.
A fully charged battery and a fully discharged battery contain exactly the same number of electrons. The difference is energy stored by the chemical manipulation (charge separation) of those internal charges.

The amount of charge separation in a fully-charged and a depleted battery is miniscule. The difference is in the potential energy associated with the different chemical compositions of the two states.

 

The amount of charge separation in a fully-charged and a depleted battery is miniscule. The difference is in the potential energy associated with the different chemical compositions of the two states.

The products of a spontaneous oxidation/reduction reaction generally yield molecules with less charge separation than the reactants (raw materials). Spontaneous, in this case, means discharge of a battery where as, non-spontaneous would be charging the battery. A nice example would be the lone electron of lithium metal in a lithium battery leaves during oxidation process snd results in a lithium ion (+) which then looks a whole lot like a tiny He atom (clearing the 2s "shell") and collapsing the electron cloud. At the same time, the oxidizing agent that takes the electron, let's say a lithium sulfur battery, so elemental Sulfur - which is a covalent (electron sharing) chain of sulfur with 8-electrons around each sulfur receives an extra electron and breaks the linear or cyclic sulfur chains to create a sulfide ion. Still with an electron configuration with a fully occupied molecular orbitals as a 2- ion as S2- or a terminal ion on a sulfide chain as one covalent bond and one additional electron. In either case, the oxidized sulfur atom (ion) will have almost the same sized electron cloud because the inner (core) electrons shield the effect of the nuclear positive proton charge from the outer electrons.
You can Google "shielding electrons" and "effective nuclear charge" for more info.

also, you can look at the density (average density) of battery materials in their charged and discharged state to get a comparative estimate of charge density. In general, solid battery materials, will have a lower density in the charged state vs the discharged state. In the example above, comparing the volume of a mole of lithium metal and a half mole of the volume of sulfur to a half mole of Li2S.

 

The amount of charge separation in a fully-charged and a depleted battery is miniscule. The difference is in the potential energy associated with the different chemical compositions of the two states.

Sure, the actual energy stored in the electric field at any instant is minuscule compared to the total energy in the potential chemical reactions. Over-time the battery redox energy is transformed to/from electrical energy during the charge/discharge cycle , the total number of electrons doesn't change.

https://pubs.acs.org/doi/10.1021/acs.jchemed.8b00479#