GR0177 #67



Alternate Solutions 
62a 20161018 23:31:52  You don\'t need to solve anything. Just observe that since the separated nuclei are given some energy, conservation of energy means their nucleons must now be more tightly bound. E fits, and none of the other choices is tenable.   QuantumCat 20140922 16:44:35  In units of MeV:
=
=
Same method as Yosun's, just a nicer look at the algebra of the problem.  

Comments 
62a 20161018 23:31:52  You don\'t need to solve anything. Just observe that since the separated nuclei are given some energy, conservation of energy means their nucleons must now be more tightly bound. E fits, and none of the other choices is tenable.
62a 20161018 23:33:01 
[the separated nuclei are given some *kinetic* energy, that is]

  nasim 20151013 17:25:25  Think of it like this:\r\nE(final)E(initial)= K and E(initial)E(final)= K   QuantumCat 20140922 16:44:35  In units of MeV:
=
=
Same method as Yosun's, just a nicer look at the algebra of the problem.   jw111 20081105 22:30:49  binding energy is negative like David said.
so
Uf+K=Ui
240X+200=7.6*240
X = 8.5
==========================
at beggining (set c = 1 ), the total energy is
Ei = Eo + Eb = Mi
Eb > mass of binding energy
Eo > rest mass energy
after fission
Ef = Eo + eb = Mf < Mi
(since Eb = 7.6*240 and eb = 8.5*240)
So the "missing mass" becomes the K   Poop Loops 20081101 20:18:31  Binding energy goes down as atomic number goes up, sort of like with electrons.
Therefore it wouldn't make sense for A = 120 to have *less* binding energy than A = 240.
Secondly, if you check 7.6 * 119 it is about 96MeV, therefore each fragment has to be *less* massive than half the original mass, because it states that their kinetic energy is now over 100MeV.
(A) I ruled out just because it seems weird. Also, Uranium does fission spontaneously, that's why it's used in reactors and bombs, etc.
(B ) I ruled out because of the previous calculation that says the 2 new masses are smaller than the whole mass before, but you can see that it's not by much, so "large" doesn't quite cut it.
askewchan 20081107 16:55:59 
Actually, binding energy goes down only after iron or so. Binding energy is lowest in Hydrogen, rises to a maximum around iron, then it goes down.
This is why energy is released by fusion for light elements, but by the opposite (fission) for heavy elements. The ultimate endpoint of both of these processes is iron, from which you can no longer milk any binding energy.

askewchan 20081107 16:57:57 
There's actually a very cool plot of this at the very bottom of the article:
http://en.wikipedia.org/wiki/Binding_energy

  jesford 20080405 11:27:03  I get answer D (6.7 MeV/nucleon) by solving Yosun's equation.... how does she get 8.5?   michealmas 20061231 10:37:21  I don't understand Yosun's use of signs! Using +200 on RHS gives answer D, but it implies that A=120 is a less stable atom than U. The famous graph of binding energy per nucleon shows that binding energy takes a maximum at Fe(the most stable atom) and decreases in both directions away from Fe. Binding energy/nucl. for A=120 must be larger than for A=238.   David 20061201 22:14:08  I believe the binding energy is a form of potential energy, and must be taken to be negative.
Remember, zero binding energy means no bond and the nucleons will just fall apart. More binding energy is more stable, so systems will tend to fall into states of greater bond energy (deeper into a potential well).   herrphysik 20060928 00:45:20  Question: why is ? Shouldn't it be +100MeV? Shouldn't the initial binding energy be larger than the final binding energy since in the latter some of the energy has been converted to kinetic? Is this an error with ETS or am I missing something?
travis.nicholson 20061023 00:41:22 
For clarity, it would be easier to write . Note that is the sum of the kinetic energies of both fragments, each of which have a . Therefore,

SonOfOle 20061031 21:38:09 
I'm with herrphysik here. With a higher binding energy per nucleon after the fission, wouldn't energy have to be added to the nuclei, not taken away in the form of KE? Anyone care to clarify this?

herrphysik 20061102 15:06:16 
I think the extra energy after fission comes from the difference in mass between uranium and the two fragments, and the fragments must have a higher binding energy because the uranium splits into more stable fragments.

mhas035 20070407 20:30:47 
Binding energy is negative, like a potential. Bigger magnitude means more negative. So a nucleon starts with it's rest mass energy then "loses" some of it when it becomes part of a nucleus. In fission the nucleons go further into the potential well (become more stable) and must release the energy they have lost (into KE in this case).

 

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