Why Does Nuclear Fusion Result in Mass Loss and Energy Release?

[patapat]

Homework Statement

In a nuclear fusion reaction two 2H atoms are combined to produce 4He.
(a) Calculate the decrease in rest mass in unified mass units.
(b) How much energy is released in this reaction?
(c) How many such reactions must take place per second to produce 400 W of power?

Homework Equations

The Attempt at a Solution

Honestly, I'm not quite sure where to begin, i think it would help best if someone could explain the the process of the nuclear fusion and why there is a decrease in rest mass. Thanks in advance.

-Pat

 

[mgb_phys]

In a nuclear fusion reaction two 2H atoms are combined to produce He.

That's pretty much all there is to fusion!
You need to have accurate values for the masses of H and He nulcei then there's an equation you might have heard of ? e=mc^2

 

[patapat]

well normally hydrogen has only one proton giving it a mass of 1.00794kg. so am i to assume there is a neutron in the hydrogen nucleus?

 

[mgb_phys]

The font you've written the equations in is a little confusing.
It should say two hydrogen H2 nuclei form a Helium He4 nuclei where the 2 and 4 are atomic masses.
So the Hydrogen here is actually Deuterium with a proton and a neutron in it's nuclei. Note that you will have to lookup the mass of a Deuterium nuclei, you cannot simple add the mass of a proton and neutron because of the very effect you are trying to measure!

 

[Astronuc]

One needs to understand binding energy with respect to fusion.
http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html

In the pp-chain, the nuclei of 4 hydrogen atoms, i.e. protons, do combine by virtue of intermediate steps to form the nuclear of a helium atom, or alpha particle. p+p -> d, the p+d -> 3He, the 3He + 3He -> 4He + 2p.

However, the net effect is 4p -> He4 + energy.

http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html

http://en.wikipedia.org/wiki/Proton-proton_chain_reaction

http://nobelprize.org/nobel_prizes/physics/articles/fusion/sun_pp-chain.html

http://zebu.uoregon.edu/~rayfrey/321/lecture5.pdf

http://burro.cwru.edu/Academics/Astr221/StarPhys/ppchain.html

http://www.astro.virginia.edu/class/hicks/astr348/lectures/lecture4.pdf