Nuclear Fission Energy and Mass Loss

[resurgance2001]

Homework Statement

When a Uranium 235 nucleus absorbs a slow moving neutron and undergoes fission one possible pair of fission fragments is technetium 112 and Indium 122. In this reaction a further 2 neutrons are emitted. Given the binding energy per nucleon of U-235 = 7.59 MeV, the binding energy of Tc - 112 = 8.36 MeV per nucleon and 8.51 MeV per nucleon of In -122 , calculate the energy released in MeV when a single nucleus of U-235 undergoes fission in this way. Note that in the reaction there is a single incoming neutron which is absorbed by the U-235 nucleus to trigger the reaction.

Relevant Equations

Energy released = Binding Energy of products - Binding Energy of Reactant

(112 x 8.36 + 122 x 8.51) - 235 x 7.59 = 190.89 MeV

My question is what should I do about the incoming neutron on the left that starts the fission. My thinking is that it does not have any binding energy and therefore I left it out of the calculation. Is that correct? Thank you

 

[Steve4Physics]

Homework Statement: When a Uranium 235 nucleus absorbs a slow moving neutron and undergoes fission one possible pair of fission fragments is technetium 112 and Indium 122. In this reaction a further 12 neutrons are emitted.

Could there be a mistake in the question? As I read it:
You start with 235+1 = 236 nucleons.
You end up with 112+122+12 = 246 nucleons.
But the number of nucleons shouldn't have changed.

 

[resurgance2001]

Could there be a mistake in the question? As I read it:
You start with 235+1 = 236 nucleons.
You end up with 112+122+12 = 246 nucleons.
But the number of nucleons shouldn't have changed.

I have edited the question. That was a typo which I have corrected. Thank you

 

[Steve4Physics]

Relevant Equations: Energy released = Binding Energy of products - Binding Energy of Reactant

(112 x 8.36 + 122 x 8.51) - 235 x 7.59 = 190.89 MeV

My question is what should I do about the incoming neutron on the left that starts the fission. My thinking is that it does not have any binding energy and therefore I left it out of the calculation. Is that correct? Thank you

Yes - that's correct. And, of course, the same applies to the two outgoing neutrons on the right.

The energy released here is entirely due to the change in binding energies – so you can ignore unbound nucleons.

You should be able to convince yourself of this by starting with 95 separate protons and 141 separate neutrons and finding the energy released when your use them to construct either:
a) an U-235 nucleus (+1 left-over neutron) or
b) a Tc-112 nucleus and an In-122 nucleus (+2 left-over neutrons).

Note, if you were given masses (rather than binding energies) you would have to consider the total masses on the left and right – which would have to include the unbound particles.

By the way, don’t forget that the final answer should be rounded to an appropriate number of significant figures.

 

[resurgance2001]

Thank you