# Mass of an electron

1. Aug 3, 2015

### Einstein Jr.

If an electron moves at light speed, how do we know that it has a definite mass(9.1 x 10^-31kg)? According to relativity, shouldn't its mass be infinite?

2. Aug 3, 2015

### Stephanus

It is its rest mass. And because electron has mass, it doesn't move at light speed. I would say near light speed. But compared to what?
[Add: much less neutrino. Its mass is much smaller than electron, and neutrino can't travel at light speed.
Only photon. Although photon has momentum]

3. Aug 3, 2015

### Einstein Jr.

What is the difference between rest mass and normal mass? Even if an electron moves at near light speed, wouldn't we get a huge value for its mass, rather than a really small value like 9.1x10^-31?

4. Aug 3, 2015

### ChrisVer

What do you mean by normal mass? there are different masses, each having a specific definition.
Here you have discussed about the relativistic mass and the rest mass...
The relativistic mass is the energy a particle has. It is equal to $m_{rel}=\gamma m_0$ where $\gamma$ the relativistic gamma factor and $m_0$ the rest mass.
The problem with this mass is that it is frame dependent (you can see that from the existence of gamma).
The rest mass is the energy a body has when seen from a reference frame that moves along with the particle (so the particle is at rest in that frame). The thing with that mass is that it's frame independent, and it's equal to the sqrt(energy^2-momentum^2) and the same for all reference frames, where the momentum and energy might change but this combination of theirs will remain unchanged..

As for whether you'd have a huge value for the relativistic mass, of course you would, because the particle would have to have way more energy (and momentum)... this doesn't change the fact that the particle in its rest frame will have a mass 9.1E-31 kg ...

5. Aug 3, 2015

### rootone

The rest mass is the mass of the object when it is 'stationary'.
That is, it is not moving at all in relation to the frame in which it is being measured.
Once it is moving within the measurement frame it has gained kinetic energy, (within the reference frame).
Energy is equivalant to mass so we can say that it's mass has increased (within the reference frame), this is it''s 'relativistic mass'.
However the increase doesn't get noticeable until approaching, light speed, and it can't actually get to light speed, just close.

In the LHC protons (which have a much greater rest mass than electrons) are accelerated to relativistic speeds, but their relativistic mass goes nowhere near infinity.
Somewhere in here I think it was said, that their mass (relativistically) becomes comparable to a small insect, like a gnat, so nowhere near infinite, but very big compared to a proton at rest.

Last edited: Aug 3, 2015
6. Aug 3, 2015

### Einstein Jr.

By normal mass I meant the way of measurement of mass that I use in everyday life. I now know that I meant rest mass. Sorry for being so unscientific :( I'm kinda new here.

Now, according to you guys, an electron orbiting an atom will have a huge mass. (this is what happens in an atom, if I'm not wrong, since it travels really fast) Therefore, shouldn't the atoms themselves also have huge masses, along with everything made of atoms?

7. Aug 3, 2015

### ChrisVer

This is not a mass again in the everyday understanding of it- it's energy, and the electrons don't "orbit" an atom fast enough (if you can talk about orbits in quantum mechanics), and so don't have to be considered relativistic.... relativistic corrections come as "corrections"...

8. Aug 3, 2015

### ChrisVer

have a look at this thread, especially this quote:
and the link attached in FAQ on the mass energy eequivalence.

Last edited by a moderator: May 7, 2017
9. Aug 3, 2015

### Staff: Mentor

Moderator's note, some off topic posts have been removed.

10. Aug 3, 2015

### Staff: Mentor

Please banish the idea of relativistic mass from your mind. A moving electron has the same mass as an electron at rest. Mass is invariant. The FAQ linked to above is a good starting point. When physicists are talking to each other they practically never mean "relativistic mass" when they say just "mass".

In an atom the electron has a small amount of KE in the ground state. This KE will contribute to the mass of the atom as a whole, but it is not specifically mass of the electron.

11. Aug 3, 2015

### Staff: Mentor

It is because of the type of confusion as the OP has, that scientists have shifted to always talk about energy, never mass except for rest mass.

Even our best scientists can get tripped up by the tricky language.
I believe that what DaleSpam should have said was "This KE will contribute to the energy of the atom as a whole." The (rest) mass of an atom does not increase when we add KE to it.

We can illustrate that by shifting the electron in the atom to a higher energy state, The energy of the atom increases but not its mass.

DaleSpam's statement was correct, but it can be misleading in this context.

12. Aug 3, 2015

### Staff: Mentor

Consider two deuterium nuclei. Do they have more, less, or the same rest mass as a single helium-4 nucleus? These two configurations contain the same number and type of particles, and differ only in their internal energy.

13. Aug 3, 2015

### Staff: Mentor

Good point, even two fully ionized duterium atoms and one helium-4 nucleus have binding energy mass discrepancies. But still adding KE to the electrons by moving them to a higher energy state does not change their rest mass does it? Dalespam's comment sounded like a nucleus capturing an electron with higher KE makes the atom have more rest mass. The excess KE of the captured electron goes to KE of the atom, not its rest mass.

14. Aug 3, 2015

### Staff: Mentor

It depends on where you place the boundaries of the system, and where the energy to excite the electron came from. In general, internal energy contributes to the rest mass of a system and energy entering or leaving the system (measured in a frame in which the system remains at rest) will cause changes in the rest mass of the system.

If you consider the entire atom to be a single system, than the excitation energy of the electrons counts as internal energy of the atom, and the rest mass of the atom will change with the absorption and emission of photons. However, when you're talking about the rest mass of the individual electrons then the system you're considering is the electron, and its rest mass does not change just because we've moved it around by adding or removing energy from the atom around it.

15. Aug 3, 2015

### Staff: Mentor

Wow! I didn't know that. I'm glad to be corrected because I learned something. Thank you Nugatory and apologies DaleSpam.

It can be very difficult to be sufficiently precise in one's language in these forums. Especially when KE is mentioned without specifying the reference frame, or when a system is discussed without defining the boundaries. I'm guilty of such inprecision.

Another recent thread [Do Protons and Neutrons Move Around In The Nucleus] talked about energy states of nuclei, and liquid drop models. From what you said, does the rest mass of a nucleus change with internal energy states?

Wikipedia quotes the "isotope mass" of Helium-4 as 4.002602 u. Is that number valid only for the ground state of the nucleus and [minimum energy] of all the electrons?

16. Aug 3, 2015

### Staff: Mentor

My wording glossed over some stuff in the middle. The KE of the electron contributes to the internal energy of the atom as a whole. The internal energy of the atom as a whole contributes to its mass. If you shift an electron to a higher energy state you do, in fact, increase the mass of the atom.

For example, if you consider a photon and an atom in its ground state in the center of momentum frame. By definition the momentum of the atom is equal and opposite to the momentum of the photon, the photon has some energy, and the atom has both internal energy and also overall KE. Now, if the photon is absorbed by the atom and excites an electron then the resulting atom is at rest in the CoM frame, and all of the energy is contained in it (the original internal energy of the atom, the KE of the atom, and the energy of the photon). Because it is at rest in the CoM frame the mass is E/c^2, which is greater than the mass of the unexcited atom.

EDIT: I see you already saw Nugatory's response.

17. Aug 3, 2015

### ChrisVer

yes. An excited nucleus would be heavier (you can have that in mind if you look at it as a system/resonance- which would later decay back to its ground state emitting energy via photons let's say).
A different example comes from hadrons, where the proton $p(938MeV)$ has an "excited state" $\Delta^+(1232MeV)$.

Also for the whole discussion I find it a bit awkward because it mixes the kinetic energy with the potential energy somehow?

18. Aug 3, 2015

### Staff: Mentor

The distinction between heat, kinetic energy, and potential energy isn't especially useful when we're talking about internal energy. If I place a compressed spring in a box and then seal the box, the rest mass of the box will not change if the spring subsequently decompresses, turning its potential energy into kinetic energy and eventually heat. All that matters is the total energy that is distributed across the various internal degrees of freedom of the box.

19. Aug 3, 2015

### Staff: Mentor

Look up the ground-state energies of the electrons and calculate their mass-equivalent. I suspect you'll find that it's less than 0.000001 u, the precision of that number.

When a hydrogen atom makes a transition from n=1 to n=2, the energy involved is on the order of 10 eV. 1 atomic mass unit corresponds to approximately 1000 MeV = 109 eV. Therefore that transition changes the mass of the atom by about 10-8 u. I don't know if it's even possible to resolve such differences experimentally. In heavier atoms, the electron energies get larger, so some effects on the mass might well become apparent, although I don't know any specific examples.

Last edited: Aug 24, 2015
20. Aug 4, 2015

### vanhees71

Just let me add one more thought, which is very important: The idea that the electrons in an atom (in stationary states) is moving, is plain wrong. The discovery of Rutherford that an atom consists of a very heavy nucleus a lot of "empty space" and "electrons around it", is incompatible with classical physics. According to classical physics the electrons should have to move around the nucleus like the planets around the Sun, but then electrons are electrically charged, and since they do not move with constant velocity but are accelerated according to Maxwell's equations of electromagnetism should lose kinetic energy due to the radiation of electromagnetic waves, and thus should crash into the nucleus after a very short time.

What's observed is pretty different: An atom in its ground state doesn't radiate at all. Neither does it collapse but is very stable (if its nucleus is not radioactive, but that's another story). This puzzle could only be solved by modern quantum theory, discovered by Heisenberg, Born, Jordan, SchrÃ¶dinger, and Dirac in 1925/26: According to this theory, the best theory we have today concerning the description of matter, the electrons do not move within the atom when the atom is in a stationary state (that's why the state is called stationary). Thus they also do not radiate and are stable, when in the state of lowest possible energy (ground state).

If the atom is in an excited state, due to the interaction with the fluctuating electromagnetic field (or by some external disturbance), it can change its state to a lower-energy state, radiating off a photon, i.e., an electromagnetic-field quantum which has the energy according to the difference of the energy levels of the atom.

21. Aug 9, 2015

### Staff: Mentor

Nugatory, DaleSpam and ChrisVer all confirmed that an excited atom has more rest mass than it's unexcited state. jtbell reminds us that this is true, but the amount of mass change is very small.

It took a while for the implications of that to sink in. All my life, I've been taught that for all evolutions, mass is conserved and energy is separately conserved. The only exceptions were nuclear reactions and cosmological scales.

But after reading this thread, I realize that virtually any chemical reaction will change the internal energy of the constituants (or of the macro cluster or crystal to which they belong), therefore strictly speaking mass-energy is conserved, but not mass and energy.

I'm an engineer, and I've been writing first principle equations with mass balance and energy balance for 50 years. Not once did anyone mention that this is an approximation, and not strictly true (except nuclear). Even if the approximation is 0.9999999 correct, it is still an approximation. 0.9999999 is good enough for engineering purposes (or for chemistry) yes, but we still like to nod to science enough to mention the difference between something that is absolutely true versus approximately true. I feel misled by my education.

Thank you all, you rattled my foundations with a bit of knowledge that may be trivial to physicists, but seems very profound in my frame of reference.