Seeking Clarity on Calculating Molar Binding Energy of Carbon-12

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Discussion Overview

The discussion centers around calculating the molar binding energy of carbon-12 nuclei, including related concepts such as binding energy per nucleon and the necessary background information for these calculations. Participants explore theoretical aspects and practical calculations relevant to nuclear physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant seeks clarification on calculating the molar binding energy of carbon-12 nuclei and requests background information.
  • Another participant explains that binding energy is derived from the mass difference between nucleons and the nucleus, referencing Einstein's equation E=mc².
  • A participant calculates the mass difference for carbon-12 and attempts to apply it to find the binding energy, but later expresses confusion about calculating binding energy per nucleon for helium-4.
  • There are discussions about the importance of using correct units, particularly converting masses to kilograms for SI units and understanding the implications of using atomic mass units.
  • One participant suggests calculating the binding energy for helium-4 by comparing the mass of its constituent nucleons to the mass of the helium-4 nucleus and dividing by the number of nucleons.
  • Participants provide useful unit conversions for atomic mass units and energy, emphasizing the need for precision in calculations.

Areas of Agreement / Disagreement

Participants generally agree on the importance of understanding binding energy and the need for careful unit conversions. However, there is no consensus on the specific calculations or methods for determining binding energy per nucleon, as some participants express confusion and seek further clarification.

Contextual Notes

Limitations include potential misunderstandings regarding unit conversions and the application of mass-energy equivalence in calculations. Some participants may lack clarity on the transition from molar binding energy to binding energy per nucleon.

Who May Find This Useful

This discussion may be useful for students or individuals studying nuclear physics, particularly those seeking to understand binding energy calculations and the underlying principles of nuclear stability.

Moe_slow
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Hey, i was ill for a few day, (damn flu) and missed some classes, am trying to catch up and need some help to understand some things.

Question:
Calculate the molar binding energy of carbon-12 nuclei.

Attempt at solution:
I don't really know where to start with this. can someone explain some terms or background information for me? thanks.
 
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The binding energy of a nucleus is the energy that holds the nucleons (neutrons and protons) together in the nucleus. This energy comes from the mass difference between the individual nucleons and the nucleus itself. The mass difference is related to the energy through Einstein's famous [tex]E=mc^2[/tex]. The molar binding energy is the binding energy of avagadros number of C-12 nuclei.
 
ok thanks. i think i understand.

so the mass of one proton is 1.0078 and neutron is 1.0086. there are six neutrons and 6 protons. that gives us 12.098940 and since the mass of the carbon 12 is 12.0000 the mass difference is 0.098940. insert that into einstein's equation and we get ((9.8x10^-5)(9.0x10^13))=8.9x10^9.moving on. can you help me understand the concept of this question.

calculate the nuclear binding energy per nucleon. 4He 4.0026u.
i don't really understand the j/nucleon part or how to get there. i tried doing it similar to the other but get a wrong answer.
 
Moe_slow said:
ok thanks. i think i understand.

so the mass of one proton is 1.0078 and neutron is 1.0086. there are six neutrons and 6 protons. that gives us 12.098940 and since the mass of the carbon 12 is 12.0000 the mass difference is 0.098940. insert that into einstein's equation and we get ((9.8x10^-5)(9.0x10^13))=8.9x10^9.

Be careful with your units. Pay attention to the fact that 1.0078g is the mass of a mole of nuclei. You want the mass in kg, for SI units (J).
calculate the nuclear binding energy per nucleon. 4He 4.0026u.
i don't really understand the j/nucleon part or how to get there. i tried doing it similar to the other but get a wrong answer.
In the above case, you found the energy for 1 mole of nuclei - that's N(avogadro) nuclei. In this problem you want to find the binding energy for a single nucleon (4 nucleons in a nucleus, and N nuclei in a mole).
 
Last edited:
As Gokul mentioned, one must be careful with units.

For binding energy of He-4, consider mass of 2p and 2n and compare to mass of He-4. Then use that to calculate the binding energy. Divide by the number of nucleons in the He-4 nucleus (4) to get BE/nucleon.

Useful units. 1 u ( or atomic mass unit, amu) = 931.494 MeV = 1.660539 x 10-27 kg

1 MeV = 1.6022 x 10-13 J, or more precisely according to NIST,
1.602 176 53(14) x 10-13 J

See - http://physics.nist.gov/cuu/Constants/index.html

See also Atomic and nuclear constants or use the values in one's textbook.
 

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