Undergrad Some Specific Questions Regarding Nuclides

[rtareen]

TL;DR

Attached is a screenshot of a page from my book (Sears & Zemansky's University Physics 14E).
I have some questions about the contents of this page.

My first question is about the mass distribution plot (43.11). Since fission involves two fragments, you would think that for each point there may be a corresponding point on the other side that is connected by a horizontal line. This is further reinforced by the fact that in the middle of the plot they say “Fission into two fragments with equal mass is unlikely”. However I’m not 100 percent sure about this, since there are no horizontal lines on the plot that emphasize the correspondence.

Second, since in fission we are going from a single nucleus with high A to 2 nuclei of lower A, the total binding energy per nucleon usually increases. I guess this energy comes from neutron bombardment? Or does it come from a decrease in mass? They don’t say.

Finally, a more general question. Is mass gained or lost with higher atomic number. Or is there no simple relationship between the mass difference and the nucleon number?

 

[mfb]

Since fission involves two fragments, you would think that for each point there may be a corresponding point on the other side that is connected by a horizontal line.

Approximately, yes. You also lose a variable number of neutrons, and fission to three components is rare but possible.

Second, since in fission we are going from a single nucleus with high A to 2 nuclei of lower A, the total binding energy per nucleon usually increases. I guess this energy comes from neutron bombardment? Or does it come from a decrease in mass? They don’t say.

Binding energy has a confusing sign. A higher binding energy means the nucleus is bound tighter, i.e. has a lower energy. Increasing the binding energy releases energy.

Finally, a more general question. Is mass gained or lost with higher atomic number. Or is there no simple relationship between the mass difference and the nucleon number?

Nuclei with higher atomic number always have a larger mass, simply from having more nucleons. Fission doesn't change the total number of nucleons, so its energy balance depends on the binding energy which is small (~1%) relative to the total mass.

 

[rtareen]

Nuclei with higher atomic number always have a larger mass, simply from having more nucleons. Fission doesn't change the total number of nucleons, so its energy balance depends on the binding energy which is small (~1%) relative to the total mass.

Thank you. I am just asking about how the mass of individual nucleons is greater than the mass of a nucleus with the same number of nucleons. I think that is the case. So let's call ($\Delta M_A$) the difference between A free nucleons and a nucleus of nucleon number A. Does this difference increase with increasing A, decrease, or something else?

 

[mathman]

Binding energy is the difference between the sum of the masses of the nucleons within the nucleus and the mass of the nucleus. The difference is maximum for Iron. This means lighter elements are created by fusion, while heavier elements need outside energy (velocity of particles in collision).

 

[vanhees71]

Have a look here:

https://en.wikipedia.org/wiki/Nuclear_binding_energy

and particularly:

https://commons.wikimedia.org/wiki/...le:Binding_energy_curve_-_common_isotopes.svg

This plot shows the binding energy per nucleon as a function of the nucleon number.

 

[snorkack]

Caution: this is the binding energy curve for common, beta stable isotopes, which indeed has a maximum at iron (56). Fission fragments are neither common nor beta stable, and do not have the same binding energy curve.