# 31.6 Binding energy  (Page 3/6)

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## What is $\text{BE}/A$ For an alpha particle?

Calculate the binding energy per nucleon of ${}^{4}\text{He}$ , the $\alpha$ particle.

Strategy

To find $\text{BE}/A$ , we first find BE using the Equation $\text{BE}=\left\{\left[\text{Zm}\left({}^{1}\text{H}\right)+{\text{Nm}}_{n}\right]-m\left({}^{A}\text{X}\right)\right\}{c}^{2}$ and then divide by $A$ . This is straightforward once we have looked up the appropriate atomic masses in Appendix A .

Solution

The binding energy for a nucleus is given by the equation

$\text{BE}=\left\{\left[\text{Zm}\left({}^{1}\text{H}\right)+{\text{Nm}}_{n}\right]-m\left({}^{A}\text{X}\right)\right\}{c}^{2}\text{.}$

For ${}^{4}\text{He}$ , we have $Z=N=2$ ; thus,

$\text{BE}=\left\{\left[2m\left({}^{1}\text{H}\right)+{2m}_{n}\right]-m\left({}^{4}\text{He}\right)\right\}{c}^{2}\text{.}$

Appendix A gives these masses as $m\left({}^{4}\text{He}\right)=\text{4.002602 u}$ , $m\left({}^{1}\text{H}\right)=\text{1.007825 u}$ , and ${m}_{n}=\text{1.008665 u}$ . Thus,

$\text{BE}=\left(0\text{.}\text{030378 u}\right){c}^{2}\text{.}$

Noting that $\text{1 u}=\text{931}\text{.}\text{5 MeV/}{c}^{2}$ , we find

$\text{BE}=\left(\text{0.030378}\right)\left(\text{931}\text{.}\text{5 MeV/}{c}^{2}\right){c}^{2}=28.3 MeV\text{.}$

Since $A=4$ , we see that $\text{BE}/A$ is this number divided by 4, or

$\text{BE}/A=\text{7.07 MeV/nucleon}\text{.}$

Discussion

This is a large binding energy per nucleon compared with those for other low-mass nuclei, which have $\text{BE}/A\approx \text{3 MeV/nucleon}$ . This indicates that ${}^{4}\text{He}$ is tightly bound compared with its neighbors on the chart of the nuclides. You can see the spike representing this value of $\text{BE}/A$ for ${}^{4}\text{He}$ on the graph in [link] . This is why ${}^{4}\text{He}$ is stable. Since ${}^{4}\text{He}$ is tightly bound, it has less mass than other $A=4$ nuclei and, therefore, cannot spontaneously decay into them. The large binding energy also helps to explain why some nuclei undergo $\alpha$ decay. Smaller mass in the decay products can mean energy release, and such decays can be spontaneous. Further, it can happen that two protons and two neutrons in a nucleus can randomly find themselves together, experience the exceptionally large nuclear force that binds this combination, and act as a ${}^{4}\text{He}$ unit within the nucleus, at least for a while. In some cases, the ${}^{4}\text{He}$ escapes, and $\alpha$ decay has then taken place.

There is more to be learned from nuclear binding energies. The general trend in $\text{BE}/A$ is fundamental to energy production in stars, and to fusion and fission energy sources on Earth, for example. This is one of the applications of nuclear physics covered in Medical Applications of Nuclear Physics . The abundance of elements on Earth, in stars, and in the universe as a whole is related to the binding energy of nuclei and has implications for the continued expansion of the universe.

## For reaction and binding energies and activity calculations in nuclear physics

1. Identify exactly what needs to be determined in the problem (identify the unknowns) . This will allow you to decide whether the energy of a decay or nuclear reaction is involved, for example, or whether the problem is primarily concerned with activity (rate of decay).
2. Make a list of what is given or can be inferred from the problem as stated (identify the knowns).
3. For reaction and binding-energy problems, we use atomic rather than nuclear masses. Since the masses of neutral atoms are used, you must count the number of electrons involved. If these do not balance (such as in ${\beta }^{+}$ decay), then an energy adjustment of 0.511 MeV per electron must be made. Also note that atomic masses may not be given in a problem; they can be found in tables.
4. For problems involving activity, the relationship of activity to half-life, and the number of nuclei given in the equation $R=\frac{\text{0.693}N}{{t}_{1/2}}$ can be very useful. Owing to the fact that number of nuclei is involved, you will also need to be familiar with moles and Avogadro’s number.
5. Perform the desired calculation; keep careful track of plus and minus signs as well as powers of 10.
6. Check the answer to see if it is reasonable: Does it make sense? Compare your results with worked examples and other information in the text. (Heeding the advice in Step 5 will also help you to be certain of your result.) You must understand the problem conceptually to be able to determine whether the numerical result is reasonable.

#### Questions & Answers

what is wave
the crust and trough form of something is called wave
kashif
If an object has no acceleration in an inertial reference frame, can you conclude that no forces are acting on it?
No unbalanced forces
Sorry, no unbalanced net force
the force acting on the object is 0N
Matins
yes
Mangeni
someone should ask questions
Matins
what is the instrument used to measure earthquake
Mangeni
seismograph or seismometer
Matins
it is used to measure the magnitude of earthquake
Matins
another question
Matins
who invented the Faraday cage and in which year was it invented
Mangeni
1836
Matins
What are the two major system units in the world
What is physical quantities
Jizel
they are physical properties that can be measured or calculated
ZIFAC
Do you mean the SI system and Imperial system? SI is used by scientists the world over (with notable exception being the USA)
Who is the father of physics
Newton.Geliliyo and Einstein is called father of physics
Neha
Newtin
Jizel
Einstein
Jizel
Ancient - Archimedes Classical Physics - Newton Modern Physics - Einstein But each of these has built on the work of predecessors. No single personality defines physics.
Thanks
Hussain
Galileo Galilie must be. He was the creator of the scientific method
Vincent
Galileo was no doubt inspirational, but the scientific method has existed for millennia. What Galileo did was prove the superiority of experimentation to just thinking (Aristotle's way). Again all noteworthy scientists
Newton galileo and Einstein
Gabriel
what is wave
a wave is a distirbance that transmits energy from one place ro another within or without a medium
Vincent
wave is the transfer of energy from one medium to another without the transfer of particles
ZIFAC
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
Joyfulsounds
wave is a disturbance or oscillation that travel through space and matter,accompanied by a transfer of energy
Ridwan
A wave is any disturbances in an elastic medium which carries energy from one point to another through a medium
abdul
what is harmonic motion
Nozyani
is a restoring force
Joyfulsounds
a wave is a disturbance and there are trasfer energy from one medium to another and travel through any space without the trasfer of particles.
Neha
a wave is a disturbance that travels or carries energy from one point to another through a medium
Wisdom
A moving disturbance in the level of a body water, undulation
Jizel
what is thermodynamics
what is thermodynamics
Charity
thermodynamics is a heat and energy significant physics
Neha
Relating to the conversation of heat into other forms of energy
Jizel
It's the science of conversion between heat and other forms of energy
ZIFAC
Are the antimatters of Hadrons also Hadrons?!Does the same rule apply to Leptons?
yes. Hadrons are the elementary particles that take part in stong, electromagnetic and weak interactions. Infact only Hadrons are involved in Strong interactions and when an anti-particle of any hadron is produced, it would be a hadron-conservations laws. Leptons are involved in weak int and follow
Lalita
what is physics
physic is a pure science that deal with behavior of matter,energy & how it related to other physical properties
Ridwan
Owk. But am are Art student.
Hussaini
Thanks a lot,Lalita
Daniel
what are the differences between reflection and refraction ?
Matins
I agree what are the difference
Kean
the physical properties of matter and energy
Kean
no
Kean
What happens when an aeroplanes window is opened at cruise altitude?
what is the minimum speed for any object to travel in time?
as per theory of relativity, minimum speed will be the speed of light
Mr.
what is physics
it is just a branch of science which deals with the reasons behind the daily activities taking place everyday in our lives. it clearly states the reason in the form of laws.
sandhya
?
lkpostpost2000@yahoo
like Newton's laws , Kepler's laws etc....
sandhya
physics is the study of motion or moving things. Usually the moving things are normal items like vars or planets but sometimes it's electricity or heat that moves.
Jake
physics is one of the most significant diciplines of natural science which describe the nature and its matter
Neha
I would describe it as the science that is interested in the fundamental laws of nature. For example, what is light, what is sound, what is electricity/magentism, what forces are at work on a specific body. The knowledge of the world around us makes it possible to fly, have cell phones, GPS, etc.
Robyn
what happens when an aeroplane takes off?
it flies
Mr.
the lift generated by the wing overcome the weight of the plane(in Newton)and a net force of upward is created
Phebilia
it is a direct application of Magnus effect (which helps in throwing curve balls) the wings of plane are made in such a way that the net flow of air is more below them rather than on their upper side. So when the plane accelerates, the flaps produce the upward lift when enough velocity is obtained
Mr.
then due to lower pressure on upper part of wings helps producing an additional lift because air flows from areaof lower to the area of higher pressure
Mr.
The engines located under the wings generate thrust .. in relation thrust is a force ... which ovwrcomes or becomes greater than the weight of the plane.. remember weight is a force Weight = m x g-2 So therefore F(thrust) becomes greater than F(weight) Even if by 1Newton the plane starts lifting o
Theophilus
what happens when a ship moves
Williams
What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
If it reduces the magnitude of the velocity, the acceleration sign is the opposite compared to the velocity.
Nicolas
yes
Williams
what is accerelation
an objects tendency to speed up over time
RayRay
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
Shii
the change in velocity V over a period of time T.
Matthew
Delta means "change in"...not period of
Shii
just kidding. it all works mathematically
Shii
except doesn't time really only change if the instantaneous speeds vary...?
Shii
and I assume we are all talking average acceleration
Shii
Hey shiii 😀
the rate of change of velocity is callaed acceleration
Amna
a=delta v/delta t
Amna
the rate of change in velocity with respect to time is acceleration
Nana
nana you r right
Indrajit
good
oguji
what is meant by lost volt
Lost volt. Lol. It is the electrical energy lost due to the nature or the envirommental conditions (temperature and pressure) that affect the cable across which the potential difference is measured.
Theophilus
What is physics?
physics is brance science concerned with nature and properties of matter and energy
George
sure
Okpara
yah....
kashif
physics is study of the natural phenomenon on the basis of certain laws and principles. it's like watching a game of chess and trying to understand its rules how it's played.
Ajit
awesome
Okpara
physics is study of nature and it's law
AMRITA
physics is a branch of science that deals with the study of matter ,properties of matter and energy
Lote
Branch of science (study) of matter, motion and energy
Theophilus