# I Photon absorption

#### dsaun777

I'm not that familiar with the current theoretical standing on how electrons "absorb" photons, as in the sense that electrons in an atom absorb photons and move from lower to higher energy states. But during the absorption of a photon the electron, if you set units of c=1, gains energy and therefore gains mass. Once It gains mass/energy it re-configures itself around a higher energy state. That electron absorbs the energy and then subsequently releases the energy to get back to its ground state. Could you consider the increase of energy an increase of mass of the electron? what determines the release of the photon?

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#### PeterDonis

Mentor
during the absorption of a photon the electron, if you set units of c=1, gains energy
Yes.

and therefore gains mass
No. "Mass" means rest mass; the concept of "relativistic mass" is out of date and is not used any more.

what determines the release of the photon?
Random quantum fluctuations. At least, that's our best current understanding. The electron in an excited state is like a radioactive atom: it will emit a photon at some point, but there's no way to predict exactly when.

#### Ibix

No. "Mass" means rest mass; the concept of "relativistic mass" is out of date and is not used any more.
Would the atom gain mass, though? Since the added energy of the electron is internal to the atom, I presume so.

#### PeterDonis

Mentor
Would the atom gain mass, though?
Yes; the rest mass of the excited state will be larger than that of the ground state. The difference will be small, but in principle it's there. However, the difference can't be attributed to an "increased mass" of a particular electron.

#### dsaun777

Yes; the rest mass of the excited state will be larger than that of the ground state. The difference will be small, but in principle it's there. However, the difference can't be attributed to an "increased mass" of a particular electron.
What is the difference between the internal gain of mass in the atom and the gain of only energy not mass of the electron?

#### PeterDonis

Mentor
What is the difference between the internal gain of mass in the atom and the gain of only energy not mass of the electron?
The atom's rest mass changes. The electron's rest mass does not.

Also, for an atom with multiple electrons, there is no way to pick out one particular electron and say that it is the one that gained the energy. All you can say is that the state of the atom as a whole changes.

#### Mister T

Gold Member
I'm not that familiar with the current theoretical standing on how electrons "absorb" photons, as in the sense that electrons in an atom absorb photons and move from lower to higher energy states.
The atom absorbs the photon.

#### Ibix

What is the difference between the internal gain of mass in the atom and the gain of only energy not mass of the electron?
For a classical particle at rest, its four-momentum is $(mc,0,0,0)$ and its mass is the modulus of this divided by $c$. If the particle is in motion at speed $v$ in the +x direction (with corresponding Lorentz factor $\gamma_v$) then its four-momentum is $(\gamma_vmc,\gamma_vmv,0,0)$. Again, its mass is the modulus of this divided by $c$, or $\sqrt{(\gamma_vmc)^2-(\gamma_vmv)^2}/c=m$ (you can work through the algebra yourself). So simply adding kinetic energy to something does not increase its mass.

Now think about two classical particles at rest. Their four momenta add, giving a total of $((m+M)c,0,0,0)$ with the obvious mass. If you accelerate them to $v$ then the same reasoning as in the previous paragraph applies and the mass doesn't change.

However, if you accelerate them to different speeds $u$ and $v$ then the total four-momentum is $(\gamma_vmc+\gamma_uMc,\gamma_vmv+\gamma_uMu,0,0)$. If you work out the modulus of this and divide by $c$ to get the mass then you will find that it has changed. The reason that this case is different from the others is that you have an extra degree of freedom here, because the particles can be moving in their joint centre of mass frame. The single particle cannot and the two particles at the same speed are stipulated not to be doing so.

Note that the above applies to classical particles, not quantum ones. However some similar analysis must apply to quantum particles because otherwise the mass of a box of hot gas would vary as its atoms absorbed and emitted photons. I don't know enough quantum to fill in the maths, unfortunately.

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#### vanhees71

Gold Member
What is the difference between the internal gain of mass in the atom and the gain of only energy not mass of the electron?
A free electron cannot simply absorb a photon due to energy-momentum conservation together with the mass-shell conditions.

In contradistinction to this an atom has excited states, i.e., it can absorb a photon (with sufficiently well adjusted energy) and get into an excited state. The rest mass of the atom is defined as its energy ($\times c^{-2}$) in the center-momentum frame of the atom. This energy is higher when the atom is in the excited state and thus also its mass is higher precisely by the energy difference between the excited and the ground state. This is the true content of the most abused formula in physics, $E=m c^2$, and that's how in fact Einstein formulated and used it.

"Photon absorption"

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