# Homework Help: Four Protons Are Fused Into An Alpha Particle, Energy Released

1. May 15, 2013

### breakingaway

(answered)Four Protons Are Fused Into Alpha Particle, Energy Released

Answered: I wasn't supposed to multiply by c2. Thank you ehild

I apologize in advance if I posted this in an incorrect format or in the wrong section. I read the rules and I believe this is the correct format/place.

1. The problem statement, all variables and given/known data
The proton-proton reaction that takes place in the Sun has the net effect of converting four protons (Mp= 1.007825 u) into alpha particles (Ma= 4.002603 u). The resulting "released" energy is shared between the kinetic energy of the alpha particles, positrons, neutrinos and gamma ray photons. Assume we could eventually design a 1.00 GW (billion watt) fusion power plant using this same reaction. Also assume that 12.5% of the "released" energy (kinetic + photon) can be converted into electrical power.
How many alpha particles would need to be fused in the reactor every second?

2. Relevant equations
binding energy:
[STRIKE]Eb=c2 * (Mnucleons-Mparticle)*931.494MeV[/STRIKE]
Eb=(Mnucleons-Mparticle)*931.494MeV/u

3. The attempt at a solution
Eb = c2 * (4*Mp-Ma)=2.2058*1024eV =3.85408*105j

Eb*12.5% = 4.8115*104j

1*109W / Eb = 2.0783*104s-1

Thank you in advance for any help anybody can provide.

Last edited: May 16, 2013
2. May 15, 2013

### ehild

In what units of mass have you calculated with?

ehild

3. May 15, 2013

### breakingaway

For the problem the mass of a proton(1.007825u) and alpha particle(4.002603u) is given in atomic mass units(u=931.494MeV). I converted to joules before doing any calculations involving power.

4. May 16, 2013

### ehild

Why did you multiplied energy by c^2?

ehild

5. May 16, 2013

### breakingaway

Well, I think you just found my mistake.

Just crunched the number without the c^2 and it came out correct.

Thank you.

6. May 16, 2013

### ehild

Yes, taking the proton mass in kg-s, m(proton)c2/(1.6 10-19(J/eV) )≈931 MeV.

ehild