How Does E=mc² Illustrate Nuclear Fission and Mass Differences?

[bjoyful]

I am trying to come up with an example to illustrate how E=mc2 applies to nuclear fission. I need to be sure to distinguish between mass and mass number. I feel like I have some thing on the brink of my mind and then I loose it. I guess I need some help as I am tired and don’t know how much longer I will be able to think! Any suggestions or sites (besides my ever faithful google:) I can visit would be great.

 

[DaveC426913]

Well, the fission of uranium results in two byproducts that, together, have less mass than the original nucleus. The missing mass is released as energy.

It's hard to discuss fission without referring to the energy/mass equation.

What rouble are you having?

 

[bjoyful]

I am writting a short essay with the following questions: Explain how E=mc2 equation applies to nuclear fission. I am to illustrate my explanation with an example, being sure to distinguish between mass and mass number, and explain how a nuclear equation differs from a chemical equation.

I have answered everything, but I am having a hard time finding the example to demonstrate my points.

In case it helps you, here is what I have written in response to the above question:
A nuclear equation produces radiation and forms completely different elements. A chemical equation has all the elements balanced on both sides. In a nuclear fission event (i.e. when a U235 atom splits), if one were to carefully measure the weights of the fission products after the event and compare them to the weight of the atom before the event, there would be a slight “mass defect”. The missing mass translates into the energy acquired in the fission products, such as their kinetic energy, which leads to heat, which is used to make energy, etc. While E=mc2 is associated with nuclear events, it applies to all events involving conservation of momentum. At the speeds we are accustomed to, which do not approach the speed of light, the mass defect is not detectable.

When Einstein invented the equation, E=mc2, he realized that for nuclear reactions mass doesn’t necessarily have to be conserved. The equation indicates that some of the mass can be converted into or released as energy. When an atom breaks a part, the two pieces together have a smaller mass that the original atom. There is a great deal of energy that holds together protons and neutrons in the nucleus. During fission, the nucleus splits and relieves some of the strain, resulting in the release of energy.

I appreicate your help!

 

[DaveC426913]

Excellent. I would change only two things:

The missing mass translates into the energy acquired in the fission products, such as their kinetic energy, which leads to heat, which is used to make energy, etc.

The byproducts can be more exotic than just momentum and heat; the energy leaves as EM energy as well.

During fission, the nucleus splits and relieves some of the strain, resulting in the release of energy.

The use of the word "strain" is a bit of a misnomer here. It is a bit misleading to suggest that "strain is relieved" in the splitting.

 

[esbo]

You know before you posted your question I thought I understood E=MC2 and nuclear
fission, however now I am not so sure.
I though that there would be some mass missing and that would explain the released
energy by E=MC2
http://en.wikipedia.org/wiki/Nuclear_fission

However looking at the above (diagram top right)

We have atomic mass 236 splitting into a 92 and 141 = 233

So OK I would say the missing mass 236 - 233, = 3 is mass which is converted into
energy -HOWEVER- the mass is not missing! You can see the three little buggers shooting off. You have 92 and 141 + 3 neutrons = 236, so we are back where
we started, no mass lost! Help!

Anyways looking deeper to find some lost mass I can say the mass of a proton is
a bit more than that of a neutron. [edit -shockingly it is actually less!]

http://www.Newton.dep.anl.gov/askasci/gen01/gen01078.htm
==================
Mass of proton : 1,6726 x 10^(-27) kg
Mass of neutron: 1,6749 x 10^(-27) kg
Mass of electron: 0,00091x10^(-27) kg

The mass of a neutron is greater than the mass of a
proton because the neutron contains a proton, contains
an electron with some subatomic particles.

neutron = proton + electron + subatomic particles

====================

So maybe the answer is in there?

I will say for starters that there needs to be a electron for every proton, and the
number of electrons is the same as the atomic number (I beleive).

So...there appear to be 3 electons gone AWOL (absent without leave). - [Edit they seem to be there actually, but I will leave that mistake in as I show below all the electrons are accounted for.]
It would need to show 3 electrons shooting off to balance the mass in my opinion,
and it does not show any.[edit - I was wrong all the electrons are accounted for]

So... I guess some of the protons have converted into neutons, which *would*
explain it, however...looking at the numbers the neutron are actually *heavier*
tham protons! So it needs to take in energy - oh dear - that seems to make things
worse! (Sorry about that!)

Atomic numbers:- (number of electrons)
UR 92 (236) = 144 neutrons

Ba 56 (141 = 85 neutrons
Kr 36 (92) = 56 neutrons
---------------
----------- 141 + the 3 loose neutron = 144

So...thats pretty hopeless the numbers don't add up.
Sorry I can't help :O))
It looks like no mass has disappeared whatsoever, I think the energy released
is something to do with 'binding' energy of the nucleus.

I would like to know the answer myself, looks like no matter is destroyed whatsoever,
maybe you should ask in the physics forum as I think it might be physics, not chemistry.

 

[esbo]

I am writting a short essay with the following questions: Explain how E=mc2 equation applies to nuclear fission. I am to illustrate my explanation with an example, being sure to distinguish between mass and mass number, and explain how a nuclear equation differs from a chemical equation.

I have answered everything, but I am having a hard time finding the example to demonstrate my points.

In case it helps you, here is what I have written in response to the above question:
A nuclear equation produces radiation and forms completely different elements. A chemical equation has all the elements balanced on both sides. In a nuclear fission event (i.e. when a U235 atom splits), if one were to carefully measure the weights of the fission products after the event and compare them to the weight of the atom before the event, there would be a slight “mass defect”. The missing mass translates into the energy acquired in the fission products, such as their kinetic energy, which leads to heat, which is used to make energy, etc. While E=mc2 is associated with nuclear events, it applies to all events involving conservation of momentum. At the speeds we are accustomed to, which do not approach the speed of light, the mass defect is not detectable.

When Einstein invented the equation, E=mc2, he realized that for nuclear reactions mass doesn’t necessarily have to be conserved. The equation indicates that some of the mass can be converted into or released as energy. When an atom breaks a part, the two pieces together have a smaller mass that the original atom. There is a great deal of energy that holds together protons and neutrons in the nucleus. During fission, the nucleus splits and relieves some of the strain, resulting in the release of energy.

I appreicate your help!

Well this is not really help, but anti-help! (bit like anti-matter but worse!)

As I hope I showed in my previous reply, no mass appears to have been lost, indeed
I mistakeny showed at one point that matter had been gained!

 

[bjoyful]

Thanks everyone you giving me input on this...

 

[esbo]

OK my latest take on this is that no matter is destroyed and that the only
possible relationship I can attribute to E=MC2 is...well none basically.
Err well wait a minute...

http://www.worsleyschool.net/science/files/emc2/emc2.html
"Two protons stuck together have less mass than two single separate protons!"

That would seem to be the key I suppose, but then you would have to qualify the
expression "mass of a proton".

 

[esbo]

I actually remember asking my chemistry teacher about this, I thought some protons
or neutrons had disappeared, but he said no it was to do with nuclear binding energy.
However I did not understand it really (at the time) the key is the particles lose (or is it gain) mass when they are combined, that energy is the binding energy, proportional
to E=MC2.