What is the Isobar Binding Energy and How Does it Affect Atom Masses?

In summary, isotopes with the same mass numbers are called isobars. The isotope 139/57 La is stable, while the radioactive isobar 139/59 Pr decays by e+ emission and the radioactive isobar 139/55 Cs decays by e- emission. The La isobar has the highest neutron to proton ratio, while the La isobar also has the greatest binding energy per nucleon. However, there may be discrepancies in atomic mass calculations due to the need for precision.
  • #1
jjson775
101
23
Homework Statement
Nuclei having the same mass numbers are called isobars. The isotope 139/57 La is stable. A radioactive isobar 139/59 Pr decays by e+ emission. Another radioactive isobar 139/55 Cs, decays by e- emission. a) Which of these 3 isobars has the highest neutron to proton ratio? b) Which has the greatest binding energy per nucleon?
Relevant Equations
See below
1605996319506.png

36FAA667-5ACC-47C7-B317-0159655CF1F2.jpeg
 
Physics news on Phys.org
  • #2
jjson775 said:
Homework Statement:: Nuclei having the same mass numbers are called isobars. The isotope 139/57 La is stable. A radioactive isobar 139/59 Pr decays by e+ emission. Another radioactive isobar 139/55 Cs, decays by e- emission. a) Which of these 3 isobars has the highest neutron to proton ratio? b) Which has the greatest binding energy per nucleon?
Relevant Equations:: See below

View attachment 272898
View attachment 272899
How are you calculating the atomic masses of the isotopes? I just looked them up, and calculate that the La has the highest binding energy, as expected for the most stable.
 
  • #3
139/59 Pr does not exist according to my table. So, to calculate the atomic mass to use in the binding formula, I used 140.908 for 141 Pr and subtracted the mass of 2 neutrons to give me an atomic mass of 138.9 for 139 Pr., as shown in the picture of my work. Apparently, my reasoning is wrong because the binding energy I get is too big.
 
  • #4
jjson775 said:
139/59 Pr does not exist according to my table. So, to calculate the atomic mass to use in the binding formula, I used 140.908 for 141 Pr and subtracted the mass of 2 neutrons to give me an atomic mass of 138.9 for 139 Pr., as shown in the picture of my work. Apparently, my reasoning is wrong because the binding energy I get is too big.
At https://onlinelibrary.wiley.com/doi/pdf/10.1002/9783527618798.app2 it is given as 138.9089322.
The problem with your approximation method is that all three will have binding energies (correction: I mean, of course, atomic masses) close to 138.9, so precision is crucial.
 
Last edited:
  • #5
Thanks. I found a reference with more precise atom masses.
 

1. What is isobar binding energy?

Isobar binding energy is the amount of energy required to break apart an isobar, which is a group of atoms with the same number of nucleons (protons and neutrons) but different atomic numbers. It is a measure of the stability of an isobar.

2. How does isobar binding energy affect atom masses?

The isobar binding energy contributes to the overall mass of an atom. When an isobar is broken apart, the energy released or absorbed affects the mass of the atoms involved. This is known as the mass defect and is accounted for in the atomic mass of elements.

3. What factors affect the isobar binding energy?

The main factors that affect isobar binding energy are the number of protons and neutrons in an isobar, as well as the nuclear forces between these particles. The stronger the nuclear forces, the higher the isobar binding energy and the more stable the isobar.

4. How is isobar binding energy measured?

Isobar binding energy is typically measured in units of MeV (mega electron volts). This measurement is obtained through experiments involving nuclear reactions, such as nuclear fission or fusion, which release or absorb energy and can be used to calculate the isobar binding energy.

5. Why is isobar binding energy important in nuclear physics?

Isobar binding energy is important because it helps explain the stability of atoms and the behavior of nuclear reactions. It also plays a crucial role in nuclear energy production and in understanding the structure and properties of atomic nuclei.

Similar threads

  • Introductory Physics Homework Help
Replies
1
Views
439
  • Introductory Physics Homework Help
Replies
10
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
1K
Replies
13
Views
349
  • Introductory Physics Homework Help
Replies
4
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
592
  • Introductory Physics Homework Help
Replies
6
Views
829
  • Special and General Relativity
Replies
5
Views
1K
  • Introductory Physics Homework Help
Replies
9
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
771
Back
Top