# E=mc^2 question

1. Oct 6, 2008

### particlex

During a nuclear reaction, some energy (or heat) radiate away, I understand that means some mass (or substance) get away. What left over is lighter. Does this mean some basic particle disappeared? for example there are less number of neutrons after the reaction? or the number of particles are conserved, but each particle becomes lighter?

2. Oct 6, 2008

### mgb_phys

Relativity says that things like mass aren;t fixed absolutes, they depend on where you are. So a particle in the nucleas can have a different mass, if some of the mass-energy goes into binding it to other particles, the same particle outside an atom can have a different mass.

Some reactions do spit out a particle, but that's not to do with e=mc^2, just the way the atom breaks up

3. Oct 6, 2008

### particlex

mgb_phys, thanks for your prompt reply. I appreciate it, But it still not answer my question, I understand the relativity, that is, when you accelerate a particle, its mass increases, because you input energy to it. The energy is converted to mass according to e=mc^2. so depending on the relative velocity to the observer, the mass are different. My question is different but related.

Let me make my question more clear: suppose we have a nuclear reactor and it is an isolated system in the sense that only heat and radiation can escape from the reactor, after the reaction, does the reactor becomes lighter? if so, are there less neutrons or protons, or there are still same number of neutrons and protons in the reactor, but they just becomes lighter compared to those before the nuclear reaction?

Thanks again.

4. Oct 6, 2008

### mgb_phys

Yes, if you take energy out of a reactor the fuel must become lighter - mass+energy is conserved even in nuclear power!

The total mass of the decay products + the neutrons is less than the original mass of the U235. The extra 'mass' goes (mostly) into the kinetic energy of the neutrons.
It's this energy that heats the water/gas and we use to drive the turbines.

No particles are lost ( actaully the reaction generates neutrinos that go stight through the walls of the reactor and also carry away a bit of energy - but we can ignore that). It's that the particles left inside the Kr / Ba / etc daughter nuclei are lighter than those in the original U235. This is due to the different stability and binding energy of theose nuclei.

This is still an effect of relativity - just not the same bit as the mass=speed.

5. Oct 6, 2008

### particlex

So the number of particle (proton or neutron) is conserved according to your answer. I also have that impression, however, I have more questions.

Sun radiates tons of energy as electromagnetic waves, these energy can be converted to mass according to e=mc^2 in principle. My question is: can these energy create a new atom, or they can only be added to mass of existing atoms? This question is important to me because it related to another question, can an atom be created out of pure engergy, or can the world be created. Can an atom be converted to energy (electromagnetic wave) completely and vice-versa?

Thanks.

6. Oct 6, 2008

### mgb_phys

You can convert energy back into matter but you need the right circumstances.

Although you can create mass, you cannot create charge ( or other conserved quantities like spin or angular momentum) so the things you can create a bit more limited.
An electron has a mass of about 500ev, a photon pair with an energy > twice that can create an electron + positron pair. Since the particles have opposite charge everything else is conserved. A photon of 1000ev is hard gamma rays.

In theory I suppose you could create a proton-anti proton pair in the same way, but you would need one hell of a high energy photon to do it!
Note that it has to be a single photon pair, you can't use lots of low energy heat from the sun and combine it to make a pair.

Last edited: Oct 7, 2008
7. Oct 6, 2008

### particlex

Do we know any single photon (hard hard gamma rays) that have enough energy to convert (transform) to a neutron which do not have an electric charge?

8. Oct 7, 2008

### lanjarote

You can not create a electron positron pair from a single photon beacase yuo can not achieve simultaneously the conservationj of the momentum and the energy for the system. You need at least a collition between two hight energy gamma ray photons. This reaction is the counterpart of the emision of two photons in opposite directions that occurs in the electron positron anniquilation.