Relativistic energy and momentum

[roman15]

Homework Statement

protons and electrons react in the following way to make an alpha particle

4p + 2e = He + 6gamma rays + 2neutrinos

the energy created by this is taken up as kinetic energy of the alpha particle, gamma rays and neutrinos. the energy of the alpha particle and gamma rays it released as heat

what is the energy released as heat by the formation of one helium nucleus? ignore the energy of the neutrinos. the mass of the proton is 1.00728u and alpha particle is 4.00150u

Homework Equations

i was confused by i didnt have the speeds of the protons and electrons during the collision so i couldn't find the kinetic energy

The Attempt at a Solution

 

[I like Serena]

i was confused by i didnt have the speeds of the protons and electrons during the collision so i couldn't find the kinetic energy

So apparently the kinetic energy is being neglected.
What else is there?

 

[roman15]

well that's all of what was given in the question
so then would the energy just be the rest energy?

 

[I like Serena]

well that's all of what was given in the question
so then would the energy just be the rest energy?

Aren't the masses of proton and helium given?
Do they add up?

 

[roman15]

ya the masses are given
proton being 1.00728u and He being 4.00150u, and 4 protons are used, so its not exactly the same, would the difference in the mass of the 4 protons and the He nucleus be the mass equivalence of the energy given off?

 

[I like Serena]

ya the masses are given
proton being 1.00728u and He being 4.00150u, and 4 protons are used, so its not exactly the same, would the difference in the mass of the 4 protons and the He nucleus be the mass equivalence of the energy given off?

Mass-energy before and after has to be the same.
So the loss of mass must have been converted into heat/gamma-rays and kinetic energy.

Conservation of momentum means that the 1 helium atom won't move much, especially since the neutrino's are supposed to be neglected.

Do you know how to calculate how much (heat) energy was created from the lost mass?

 

[roman15]

ya the energy would just be
Heat=E=m(lost)c^2

 

[I like Serena]

ya the energy would just be
Heat=E=m(lost)c^2

I was kind of going for something like: Yes! Now I understand and I have the answer...

Actually I think a little more heat energy is released due the nucleon binding energy (strong force) and the electron binding energy (electromagnetic force).
I've looked up those contributions (wikipedia) and they would be 7 MeV resp. 80 eV.
Since they aren't mentioned, I presume they are neglected again.

Btw, what happened to the electron mass?

 

[roman15]

lmao, I am sorry i wasnt more excited, but i really do appreciate the help
and i was thinking the same thing about the electrons, but i think that since electrons are so much smaller than protons, its affect will be insignificant
once again thanks so much!

 

[roman15]

actually i just checked, it does make a significant difference with the electrons
ill probably just ask my professor about that, cause he didnt specify in the question that we consider the mass of the electrons too

 

[I like Serena]

actually i just checked, it does make a significant difference with the electrons
ill probably just ask my professor about that, cause he didnt specify in the question that we consider the mass of the electrons too

If you look carefully at the problem statement, the electrons are accounted for.
It's not the mass of Helium that is given, but the mass of the alpha particle (without electrons).
So we have 2 electrons on the left side, and an Helium atom (including 2 electrons) on the right side.