# Energy of electron and its effective mass

## Main Question or Discussion Point

Could somebody tell what is connection
between effective mass of electron and
its energy?
As I know rest energy of electron is about
500 KeV what is pretty big.
In some materials effective mass of electron
is one thousand of its rest mass.
Could we create some energy storage device
which would play on difference of effective
mass of electron in different materials?

Related Quantum Physics News on Phys.org
I would be glad to know if it's possible to create
high energy storage device which would use
unusual properties of electrons such as zero
effective mass in graphene.If electrons in two
different materials have very different effective
mass and therefore energy how could we use it?
Having different effective masses in different materials does not change the TOTAL energy of an electron supposing that the electron passes through these materials.

It's the still the same total energy, but the electron will simply change its kinetic energy, thus speed.

This is like climbing an incline --- I don't see how you can use that energy for storage??

Am I missing what you imply here?

Last edited:
Dr Transport
Gold Member
The effective mass in a crystal is related to the band structure and the energy bands curvature at the center of the Brillouin zone.

It's the still the same total energy, but the electron will simply change its kinetic energy, thus speed.

I just thought that we have different Fermi energy in different materials and this is also connected to speed of
electrons,if I no make mistake,and we could create energy
storage which uses difference between those energies.
This is usual electrochem. batteries.So I thought that we
may try to use the same principle related to different
effective mass of electron.If effective mass doesn't really
related to energy then things are different.
Also in graphene electrons seems to slow down if they
gain energy.Could we influence those electrons so they
will gain more energy and slow down and thus store energy?

It's the still the same total energy, but the electron will simply change its kinetic energy, thus speed.

I just thought that we have different Fermi energy in different materials and this is also connected to speed of
electrons,if I no make mistake,and we could create energy
storage which uses difference between those energies.
This is usual electrochem. batteries.So I thought that we
may try to use the same principle related to different
effective mass of electron.If effective mass doesn't really
related to energy then things are different.
Also in graphene electrons seems to slow down if they
gain energy.Could we influence those electrons so they
will gain more energy and slow down and thus store energy?
No, the energy storage is not possible in your sense. But you probably know of chemistry where the energy can be stored in complex molecules. Gun powder, dynamite, etc., all are the energy stores.

With different electron mass in different materials you can make contact phenomena - thermoelectric current, diodes, lots of electronic devices, etc.

Bob_for_short.

I wander if there is some possibility to create an energy
storage which would be more dense than chemical but
will not be nuclear?Or there is some serious theoretical
limits which make such storage impossible?
Is difference in Fermi energies between different atoms
maximum that we could attain?And thus Boron is the ultimate energy storage (per volume) which isn't nuclear?

I wander if there is some possibility to create an energy
storage which would be more dense than chemical but
will not be nuclear?Or there is some serious theoretical
limits which make such storage impossible?
Is difference in Fermi energies between different atoms
maximum that we could attain?And thus Boron is the ultimate energy storage (per volume) which isn't nuclear?
Okay, you are right in the sense that the potential energy of a moving electron changes when it passes through different media. So there's at least energy conversion (potential to kinetic)

But, it has to be a tangible storage, how will you transform that potential energy into something useful?

Every storage mechanism has a well-defined read-out operation. IN batteries, you transform the stored energy into electric current, in capacitors stored electric charge is read-out by current flow, in spin RAMs, magnets store the information and they interact with current flow via GMR, etc...

So, propose a device-like structure where you can actually sense (read-out) the potential energy change of a moving electron. It doesn't make sense right?

So, propose a device-like structure where you can actually sense (read-out) the potential energy change of a moving electron.

I would just patent it.
But fist of all I'm trying to understand how much energy
would be able to yield such device.
It would be interesting to create something more energy dense than chemical processes to make it competitive.
Could there be solids in which electron has very different
TOTAL energy?

Last edited:
I remember that a mix of two different metal powders compressed to a solid tablet can contain a huge energy. When you ignite a piece of it, the chemical reaction starts and the whole tablet gets very hot. Kind of melting and dissolving two metals. Something similar is possible with ceramics.

I do not have any references, it is an old recollection from my studentship.

Bob_for_short.

Last edited:
So, propose a device-like structure where you can actually sense (read-out) the potential energy change of a moving electron.

I would just patent it.
But fist of all I'm trying to understand how much energy
would be able to yield such device.
It would be interesting to create something more energy dense than chemical processes to make it competitive.
Could there be solids in which electron has very different
TOTAL energy?

Well, for that you need INELASTIC processes, which involve energy exchange, and of course, this goes to batteries, diodes, solar cells, etc...

But simply putting two different materials and assuming no other interactions won't cut it. Remember it's still the same electron, but swimming in a different water, that change may not even be measurable, experimentally speaking.

Maybe if f5toli sees this he could comment on this, he might give a different input.

But to me, it doesn't make sense. You have a pretty general idea, try narrowing it down.

Okay, you are right in the sense that the potential energy of a moving electron changes when it passes through different media. So there's at least energy conversion (potential to kinetic)
So as I've understood we need to have system which changes its own energy in WHOLE.
In this case we probably will need to have two different
materials where electron have different TOTAL energy.
Or one material in which electron could have different
energy values.
Unfortunately, electrons are not vehicles themself,otherwise
we would be able to gain from conversion of their potential
energy into kinetic.
I read that some company promises to create electronically pumped Betavoltaic batteries which would not be
radioactive by itself.Although I don't believe in possibility of it.

Last edited:
There is something interesting about graphene yet:
"In a normal electronic system such as a semiconductor, the Fermi energy" — the energy of the carriers' highest occupied quantum state when the temperature is absolute zero — "is proportional to the density of the carriers," "But in a system of 2-D Dirac fermions, the Fermi energy is proportional to the square root of the carrier density."
If I no make mistake Fermi energy have some relation
to energy capacity of batteries.Could we use graphene as
one of the components of battery?