How Do You Calculate Binding Energy Per Nucleon for Helium-4?

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SUMMARY

The binding energy per nucleon for Helium-4 (4He) is calculated using the mass defect and Einstein's equation E=Δmc². The mass defect (Δm) is determined to be 0.02928u, which must be converted to kilograms (1u = 1.66x10^-27kg) for accurate energy calculations. The total binding energy of the nucleus is found to be -2.6352x10^15 J, leading to a binding energy per nucleon of -1.13x10^-12 J/nucleon. This calculation illustrates the average energy required to remove a nucleon from the nucleus.

PREREQUISITES
  • Understanding of mass defect in nuclear physics
  • Familiarity with Einstein's equation E=Δmc²
  • Knowledge of atomic mass units (u) and their conversion to kilograms
  • Basic concepts of nucleons, including protons and neutrons
NEXT STEPS
  • Learn how to convert atomic mass units to kilograms accurately
  • Study the concept of nuclear binding energy in different isotopes
  • Explore the implications of binding energy on nuclear stability
  • Investigate the calculation of binding energy for other elements using similar methods
USEFUL FOR

Students in nuclear physics, educators teaching atomic structure, and researchers interested in nuclear binding energy calculations.

deezer
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Homework Statement



Calculate the binding energy per nucleon for 4He. Mass is 4.0026u


Homework Equations



E=Δmc^2

The Attempt at a Solution



This is my plan of attack,
first find the Δm.
Mnucleon-Mnucleus [Are these terms right? Nucleon - Nucleus ?]
Δm=4.0026u-(2p+2n)=-0.02928u

E=Δmc^2
=-2.6352x10^15J/nucleus

But the question asked for J/nucleon and I'm not sure what to do now. The correct answer is -1.13x10^-12J/nucleon.
 
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u is the atomic mass unit, convert it to kg-s.

ehild
 
Nucleons are the particles in a nucleus. That is the protons and neutrons
 
So what do I need to change? Isn't nucleon the nucleus, since the nucleus=protons+neutrons.
 
A He nucleus contains 2 protons and 2 neutrons. Your calculation of Δm is perfectly correct (0.02928u) but you need to convert u into kg. (1u = 1.66x10^-27kg)
Then use that mass in E = mc^2 to calculate the energy equivalent of this mass defect.
This is the energy holding all of the nucleons (protons and neutrons) in the nucleus.
This is called the BINDING ENERGY OF THE NUCLEUS.
Can you see how to get the BINDING ENERGY OF A NUCLEON ?
 
technician said:
A He nucleus contains 2 protons and 2 neutrons. Your calculation of Δm is perfectly correct (0.02928u) but you need to convert u into kg. (1u = 1.66x10^-27kg)
Then use that mass in E = mc^2 to calculate the energy equivalent of this mass defect.
This is the energy holding all of the nucleons (protons and neutrons) in the nucleus.
This is called the BINDING ENERGY OF THE NUCLEUS.
Can you see how to get the BINDING ENERGY OF A NUCLEON ?

It's the same thing?
 
No... He nucleus contains 4 nucleons. The binding energy PER NUCLEON is the binding energy of the NUCLEUS/4.
It is a way of giving an 'average' binding energy of NUCLEONS and makes analysing Binding energy of all of the NUCLEI easier.
You have got the idea.
The Binding energy PER NUCLEON = Binding energy of NUCLEUS/Number of nucleons
 

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