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

• deezer
In summary, the binding energy per nucleon for 4He can be calculated by first finding the mass difference between the nucleus and the individual nucleons, converting it to kilograms, and then using this value in the equation E=mc^2 to calculate the binding energy of the nucleus. To find the binding energy per nucleon, this value is divided by the number of nucleons in the nucleus. This is a way of giving an average binding energy of nucleons and makes analysis of binding energy of different nuclei easier.
deezer

Homework Statement

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

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.

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

What is binding energy?

Binding energy is the amount of energy required to break apart the nucleus of an atom into its constituent parts. It is the energy that holds the nucleus together.

Why is binding energy important?

Binding energy is important because it helps to explain the stability of atoms and the process of nuclear reactions. It also plays a crucial role in the understanding of nuclear power and nuclear weapons.

How is binding energy calculated?

Binding energy is calculated using the famous equation E=mc², where E is the binding energy, m is the mass defect (difference between the mass of the nucleus and the sum of its individual particles), and c is the speed of light. The binding energy is equal to the mass defect multiplied by the speed of light squared.

What factors affect the binding energy of an atom?

The binding energy of an atom is affected by the number of protons and neutrons in the nucleus, as well as the nuclear force that holds these particles together. Generally, larger nuclei have higher binding energies due to the stronger nuclear force.

Why is it important to know the binding energy of an atom?

Knowing the binding energy of an atom is important for understanding the stability and properties of an atom. It also helps in predicting the outcome of nuclear reactions and determining the amount of energy released or absorbed during these reactions. Additionally, the binding energy of an atom is a key factor in nuclear power and nuclear fission processes.

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