# Mass increase due to received photon

1. Dec 17, 2015

### intervoxel

Does molecular mass increase due to angular momentum (h_bar) received from photon since now we have objects rotating inside the molecule?

2. Dec 17, 2015

### ande4jo

I would expect that it would increase the mass because the energy would increase due to photon energy equal to h x f being added to the system. Molecular mass would always have objects rotating inside the molecule even before the photon gets absorbed since molecules are made up atoms that have electrons rotating constantly. Note also that sometimes the photon gets absorbed initially and the system reradiates another photon of same frequency which then would set energy state back to original value. At least that's how I invision it but I am not a physicist, just an engineer like Howard Walowitz (Big Bang reference) ☺

3. Dec 17, 2015

### dlgoff

4. Dec 17, 2015

### Staff: Mentor

Its a subtle issue. Strictly speaking E=MC^2 says mass is a form of energy, like chemical energy is a form of energy, or potential energy is a form of energy etc etc. It does not say energy is a form of mass. That said if an object absorbs a photon it has gained energy and unless it is converted to some other form like heat or kinetic energy its mass must increase.

This is because of what energy is, which requires the beautiful Noethers Theorem to fully understand:
http://math.ucr.edu/home/baez/noether.html

A staff mentor has posted when he lectures students about this there is usually stunned silence as its import sinks in.

If anyone wants to pursue Noether's amazing theorem further start a thread. Its one of the deepest, most striking, and most beautiful results in all of physics. What it means it also very deep (basically it means QM is the essence of all things - but understanding that requires some explanation).

Thanks
Bill

5. Dec 17, 2015

### Staff: Mentor

It's not the angular momentum received from the photon that does it, it's the energy.

But with that said.... yes, all else being the same, the mass of an excited molecule is very slightly greater than the mass of the same molecule when it's not excited.

6. Dec 18, 2015

### intervoxel

Where does this energy to rotate the molecule comes from since, imagine, the energy is given by a very weak absorbed photon which is entirely used to impart a very weak linear momentum and consequently very weak kinetic energy while, on the other hand, the rotation may require lots of energy?

7. Dec 19, 2015

### Hornbein

Yes, the relativistic mass increases, but the rest mass does not. The m in E=mc^2 is relativistic mass. Nowadays mass usually means rest mass and a different formula is used. It can be confusing. Definitions may change over time. You just have to deal with it.

What you are discussing is what Einstein had in mind when he originally wrote that formula. He thought that the increase in mass would be too small to be measured, so he actually wrote E/c^2=m to emphasize the tiny amount involved. He, and almost all other scientists prior to the 1930's, thought that rest mass could never be converted to energy.

8. Dec 19, 2015

### dlgoff

9. Dec 19, 2015

### Staff: Mentor

A photon may carry some amount of angular momentum, and this angular momentum will be transferred to the atom that absorbs it. But that's all the increase in angular momentum that happens. I'm not sure what you're thinking of when you say "rotate the molecule" - absorbing a photon and exciting an electron or so does not produce rotations that "require lots of energy".

10. Dec 20, 2015

### intervoxel

I'm not talking about the orbital angular momentum carried by the beam containing the photon. It's about that intrinsic, exact, value of one h_bar that must be absorbed by the receiver when a single photon disappears. It logically implies that something must alter its rotational state. Depending on the moment of inertia, it can require a lot of energy.

11. Dec 20, 2015

### Staff: Mentor

That's where the ΔJ = ±1 selection rule comes from.

That's provided by the photon. Rotational transitions are mostly in the microwave part of the EM spectrum.