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

[deezer]

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.

 

[ehild]

u is the atomic mass unit, convert it to kg-s.

ehild

 

[technician]

Nucleons are the particles in a nucleus. That is the protons and neutrons

 

[deezer]

So what do I need to change? Isn't nucleon the nucleus, since the nucleus=protons+neutrons.

 

[technician]

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 ?

 

[deezer]

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?

 

[technician]

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