I Doubling Ionization of Tungsten: Effects on Energy?

[illisil]

TL;DR Summary

Ionization and the relationship to kinetic energy

Lets say that i have i mole of tungsten atoms. They are all ionized, only one electron is removed from each atom. If i accelerate this mole of tungsten atoms through one electron volt, i would get 96.48 kj. If the mole of tungsten was doubly ionized, two electrons removed from each atom, and accelerated through one ev, would i get twice the kilojoules?

 

[Cutter Ketch]

The short answer is yes.

One persnickety comment: electron volts is a unit of energy. I think you meant one volt of electric potential.

One caveat: it would be cleaner to ask the question about a single atom rather than a mole of atoms. With many charged particles you will have to think about their mutual repulsion, and then the potential would depend on their density. The problem is that at any practical lab scale density of a whole mole of ionized atoms would have mutual repulsion so strong your one volt potential would be completely negligible in comparison. However, I get what you meant.

Even if the potential is dominated by their mutual repulsion, the idea that, given the same initial configuration, twice the charge gives twice the energy is still true. So your idea is still correct. Just, in that case, the 1 volt becomes unimportant.

Anyhow, rephrasing it, a doubly ionized atom falling through one volt of electric potential will gain twice as much kinetic energy as a singly ionized atom falling through the same potential.