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

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Homework Help Overview

The discussion revolves around calculating the binding energy per nucleon for the helium-4 nucleus, specifically focusing on the mass defect and its conversion to energy using the equation E=Δmc². The original poster presents their calculations and expresses uncertainty about the conversion of units and the interpretation of nucleons versus the nucleus.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the calculation of the mass defect (Δm) and the need to convert atomic mass units to kilograms. Questions arise regarding the terminology of nucleons and the nucleus, with some participants clarifying the definitions and relationships between these terms.

Discussion Status

Some participants have provided guidance on the necessary conversions and clarified the distinction between binding energy of the nucleus and binding energy per nucleon. There is an ongoing exploration of how to derive the binding energy per nucleon from the total binding energy of the nucleus.

Contextual Notes

The original poster is working within the constraints of a homework assignment, which may impose specific requirements for unit conversions and definitions. There is a noted confusion regarding the terms used in the calculations, particularly concerning nucleons and the nucleus.

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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