Binding energies and decay energy.

In summary, binding energy is defined as the energy required to break apart a nucleus into its individual constituents, while decay energy is the energy released when a nucleus decays into a more stable state. The difference in binding energy between a parent nucleus and its daughter nucleus is expected to be equal to the decay energy, but in the case of 53Fe decaying to 53Mn, there is a difference of approximately 4.5 MeV. This is because the decay energy calculation does not take into account the kinetic energy of the emitted electron during electron capture, and the daughter nucleus may not always be in the ground state after the transition.
  • #1
Pigkappa
22
1
I'm having some trouble with the definition of binding energy and decay energy.


Consulting a nuclide table (http://atom.kaeri.re.kr/ton/nuc5.html) I found out that 53Fe has a binding energy of 458380.194 +- 2.107 keV and decays to 53Mn by electron capture. The decay energy is 3.743 MeV and the binding energy of 53Mn is 462904.899 +- 1.439 keV .

I expect the difference in binding energy to be equal to the decay energy, but it is [tex]\approx 4.5[/tex] MeV (with relative error [tex]< 0.01[/tex]) which is quite different from 3.743 MeV.
Why aren't they the same?
 
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  • #2
Did you consider the electron?

Is teh daughter nucleus in the ground state after the transition?
 
  • #3
Pigkappa said:
I'm having some trouble with the definition of binding energy and decay energy.
Why aren't they the same?
They are two completely different things.
 
  • #4
What are their definitions then?

I thought that the binding energy B = mass of constituents - mass of the nucleus

and Decay energy = energy (mass + kinetic) of emitted particles except the mass of the new nucleus
 

Related to Binding energies and decay energy.

What is binding energy?

Binding energy is the energy required to hold together the nucleus of an atom. It is the difference between the mass of an atom and the sum of the masses of its individual protons and neutrons.

Why is binding energy important?

Binding energy is important because it is what holds the nucleus of an atom together and determines the stability of an atom. It also plays a crucial role in nuclear reactions and processes such as nuclear fusion and fission.

What factors affect binding energy?

The factors that affect binding energy include the number of protons and neutrons in the nucleus, the nuclear force between nucleons, and the strong and weak nuclear forces.

What is decay energy?

Decay energy is the energy released when an unstable nucleus undergoes radioactive decay and transforms into a more stable state. This energy is often released in the form of gamma rays, alpha particles, or beta particles.

How is binding energy related to decay energy?

Binding energy and decay energy are closely related. In nuclear reactions, the difference between the binding energy of the reactants and the binding energy of the products is equal to the amount of decay energy released during the reaction. This relationship is described by Einstein's famous equation, E=mc².

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