# Does the mass of an electron change with its “energy state”?

When an electron absorbs a photon, it gets into a higher energy state and goes into the upper orbit/shell.

Does (rather should) this absorption of energy also have an impact on its mass (although incredibly small)?

Can we even measure the mass of an electron while it is it still bound to the nucleus?

• Depends on which mass you are refering to..are you speaking on Gravitational Mass or Inertial Mass or Rest Mass? – Aron Dec 1 '14 at 17:09
• @Aron That is a highly misleading statement. I'm even tempted to say that it is downright wrong since - as far as we know - inertial mass and gravitational mass are the same. Moreover, unless you are trying to distinguish them with some major subtelty (like the mass-energy density) rest mass is also equivalent to the other two terms. I'm not sure what you are trying to get at, but I think it is really confusing the issue at hand. – Geoffrey Dec 1 '14 at 23:57
• @Geoffery. You are very wrong. Rest mass and inertial mass is NOT equivalent, except when at rest. Simple SR. Yes, inertial mass and gravitational mass is equivalent in massive particles to a few ppm, but i am not sure about concepts like holes. – Aron Dec 2 '14 at 0:18
• @Aron No, you are very wrong. By the equivalence principle of GR inertial and gravitational masses are exactly the same. And they are equal to rest mass. If you show otherwise, it'll be a major discovery. – Ruslan Dec 2 '14 at 5:53
• Just to add that, for electrons interacting with a lattice of atoms (most notably in semiconductors), there is also the concept of "effective mass" to be considered. It's just a device to summarize the effect of the interaction (more or less like 'relativistic mass'), but it comes in handy when dealing with crystals. – Peltio Dec 2 '14 at 8:13

This is really an extended comment to Geoffrey's answer, so please upvote Geoffrey's answer rather than this.

The mass of a hydrogen atom is $1.67353270 \times 10^{-27}$ kg. If you add the masses of a proton and electron together then they come to $1.67353272 \times 10^{-27}$ kg. The difference is about 13.6eV, which is the ionisation energy of hydrogen (though note that the experimental error in the masses isn't much less than the difference so this is only approximate).

This shouldn't surprise you because you have to add energy (in the form of a 13.6eV photon) to dissociate a hydrogen atom into a free proton and electron, and this increases the mass in accordance with Einstein's famous equation $E = mc^2$. So this is a direct example of the sort of mass increase you describe.

However you can't say this is an increase of mass of the electron or the proton. It's an increase in mass of the combined system. The invarient masses of the electron and proton are constants and not affected by whether they're in atoms or roaming freely. The change in mass is coming from a change in the binding energy of the system.

A particle's rest mass never changes. It's mass is a natural constant, and one of the numbers which uniquely identifies it (like its spin). On the other hand, the invariant mass of the atomic system does increase as the electron becomes excited, bringing the atom into a higher energy state. In that sense, the atom (not the electron) gets "heavier" because of the increased energy of the internal configuration of particles.

• So the atom on the whole gets heavier while the material of is composition remain at the same mass? By material I mean it's particles. So the increment in overall mass of a photon absorbing atom increases due to it's energy component instead of particles' mass increment? – Youstay Igo Dec 2 '14 at 20:04
• Basically, yes. The conceptual explanation relies on the whole $E=mc^2$ idea. Roughly speaking, the increased energy of the atom translates into an increased mass of the atom through relativistic effects. I think that John's answer is an excellent explanation. – Geoffrey Dec 2 '14 at 20:11

In the example you site, you are talking about a bound electron. In this case, the electron does not gain (any kind of) mass because the energy of the photon goes into changing the state of the electron (to a higher energy state). This energy is "given back" when the electron returns to its previous state, giving off an equivalent photon.

Even a free electron gets heavier under the influence of accelerating photons. Best example are colliders where some amount of photons energy stay on the electron and some amount the electron looses again. Then faster the electron then higher the loose. Physics lives from models and interpretations and your interpretation is nice. It brings closer together the terms energy and mass.

• Only correct if you use a text from the Eisenhower administration (to quote a Physics SE regular). The invariant mass remains invariant. Nor is this answer helpful for a bound electron which does not have a well defined momentum. – dmckee Dec 1 '14 at 22:59
• I thought there is no such thing as "invariant mass" as all matter of our universe is in a state of constant motion. So all "rest masses" are a bit misleading if you keep the bigger picture of cosmos in view. No? – Youstay Igo Dec 2 '14 at 20:09
• @YoustayIgo: Nice. – HolgerFiedler Dec 2 '14 at 20:12
• @YoustayIgo This idea which you explain in you comment here is a common misconception caused by this thing people hear about moving particles becoming more massive. Under Special Relativity a fast-moving particle is generally harder to accelerate than Newton's Laws would predict which has often - and misleadingly - been described as an increase in the mass of the particle when, in reality, it is simply a fact of Relativistic Mechanics that it isn't Newtonian Mechanics. Relativity is a brave new world. Embrace it on its own terms. – Geoffrey Dec 2 '14 at 20:53
• @YoustayIgo The invariant mass of a particle or system is defined as the length of the energy-momentum four vector. As such it is a Lorentz scalar and is measured to be the same in any frame of reference. All Lorentz scalars (including the proper-time) have that property, so people who are serious about relativity lean heavily on them because they simply all kinds of computations. A large fraction of relativists only talk about invariant mass, eschewing as unnecessary, obsolete and confusing the notion of "relativistic mass"; which is not to say that this concept can't be defined and used. – dmckee Dec 3 '14 at 20:19

I performed an experiment to take data on frequency of circular motion (f) and how it relates to the length (L) of a pendulum. In the experiment the pendulum is displaced through large angle to perform horizontal circle. Ten revolution is timed.

From the observation it is showing that the frequency, f, is inversely proportional to the length, L, of the pendulum, but directly proportional to the velocity, v, of the circular motion.

f--_ kV/L. Introducing f--_w/2pi and V--rw f-- V/2pirL . From this equation frequency is inversely proportional to the radius, r,.

This mathematics from my experiment had implications on the atom and its electrons that: 1. Electrons close to the nucleus have high kinetic energy and they move at high velocity while those that are far have high potential energy and they move at low velocity. So, kinetic energy decreases as the radius increases. 2. It confirms the uncertainty principle which focuses on the position and momentum of the electrons and its location at a given time. Electrons close to the nucleus have large momentum so uncertainty of their position is high, but those electrons that are far from the nucleus have less momentum so uncertainty of their momentum is high. This is caused by the frequency of their circular motion. 3. The observation explain why the size and mass of atoms increase down a group in the periodic table because the radius of the atoms increases while the frequency of the circular motion of the electrons decreases. 4. The observation point to the fact that the mass and size of electrons depend on their distance from the nucleus , hence electrons in the same atom have varied masses, though the difference is insignificant and are of different sizes. So, electrons have size though they may be point--like particles. I am still working on the experiment. This experiment explains some absurdities in the solar systems and its arrangement.

My name is Dzidza Mawuli Yao Emmanuel From Ghana in West Africa. Living in Volta Region. Teaching in Some Senior High School, Agbozume--Ketu South District. E-mail: edmydzidza@gmail.com