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What is BE / A size 12{ {"BE"} slash {A} } {} For an alpha particle?

Calculate the binding energy per nucleon of 4 He size 12{"" lSup { size 8{4} } "He"} {} , the α size 12{α} {} particle.


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


The binding energy for a nucleus is given by the equation

BE = { [ Zm ( 1 H ) + Nm n ] m ( A X ) } c 2 .

For 4 He size 12{"" lSup { size 8{4} } "He"} {} , we have Z = N = 2 size 12{Z=N=2} {} ; thus,

BE = { [ 2 m ( 1 H ) + 2 m n ] m ( 4 He ) } c 2 .

Appendix A gives these masses as m ( 4 He ) = 4.002602 u , m ( 1 H ) = 1.007825 u , and m n = 1.008665 u size 12{m rSub { size 8{n} } =0 "." "008665"`" u"} {} . Thus,

BE = ( 0 . 030378 u ) c 2 . size 12{"BE"= \( 0 "." "030378 u" \) c rSup { size 8{2} } } {}

Noting that 1 u = 931 . 5 MeV/ c 2 size 12{"1u"="931" "." "5 MeV/"c rSup { size 8{2} } } {} , we find

BE = ( 0.030378 ) ( 931 . 5 MeV/ c 2 ) c 2 = 28.3 MeV . size 12{"BE"= \( 0 "." "030378" \) \( "931" "." "5 MeV/"c rSup { size 8{2} } \) c rSup { size 8{2} } ="28" "." 3" MeV"} {}

Since A = 4 size 12{A=4} {} , we see that BE / A size 12{ {"BE"} slash {A} } {} is this number divided by 4, or

BE / A = 7.07 MeV/nucleon . size 12{"BE"/A=7 "." "07"" MeV/nucleon"} {}


This is a large binding energy per nucleon compared with those for other low-mass nuclei, which have BE / A 3 MeV/nucleon . This indicates that 4 He is tightly bound compared with its neighbors on the chart of the nuclides. You can see the spike representing this value of BE / A for 4 He on the graph in [link] . This is why 4 He is stable. Since 4 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 α 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 He unit within the nucleus, at least for a while. In some cases, the 4 He escapes, and α decay has then taken place.

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There is more to be learned from nuclear binding energies. The general trend in BE / A size 12{"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.

Problem-solving strategies

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 β + size 12{β rSup { size 8{+{}} } } {} 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 = 0.693 N t 1 / 2 size 12{R= { {1 "." "693"N} over {t rSub { size 8{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
Mubarak Reply
the crust and trough form of something is called wave
If an object has no acceleration in an inertial reference frame, can you conclude that no forces are acting on it?
Von Reply
No unbalanced forces
Sorry, no unbalanced net force
the force acting on the object is 0N
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seismograph or seismometer
it is used to measure the magnitude of earthquake
another question
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Jizel Reply
What is physical quantities
they are physical properties that can be measured or calculated
Do you mean the SI system and Imperial system? SI is used by scientists the world over (with notable exception being the USA)
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Gabriel Reply
Newton.Geliliyo and Einstein is called father of physics
Ancient - Archimedes Classical Physics - Newton Modern Physics - Einstein But each of these has built on the work of predecessors. No single personality defines physics.
Galileo Galilie must be. He was the creator of the scientific method
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
what is wave
Charity Reply
a wave is a distirbance that transmits energy from one place ro another within or without a medium
wave is the transfer of energy from one medium to another without the transfer of particles
wave is a disturbance which transfer energy from one medium to another without causing any permanent displacement by itself
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A moving disturbance in the level of a body water, undulation
what is thermodynamics
Williams Reply
what is thermodynamics
thermodynamics is a heat and energy significant physics
Relating to the conversation of heat into other forms of energy
It's the science of conversion between heat and other forms of energy
Are the antimatters of Hadrons also Hadrons?!Does the same rule apply to Leptons?
Daniel Reply
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
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physic is a pure science that deal with behavior of matter,energy & how it related to other physical properties
Owk. But am are Art student.
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I agree what are the difference
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Theophilus Reply
what is the minimum speed for any object to travel in time?
Pankaj Reply
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what is physics
Lote Reply
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like Newton's laws , Kepler's laws etc....
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Kofi Reply
it flies
the lift generated by the wing overcome the weight of the plane(in Newton)and a net force of upward is created
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
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
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
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What is the sign of an acceleration that reduces the magnitude of a negative velocity? Of a positive velocity?
Conwil Reply
If it reduces the magnitude of the velocity, the acceleration sign is the opposite compared to the velocity.
what is accerelation
John Reply
an objects tendency to speed up over time
acceleration is the change in velocity over the change in time it would be written delta-v over delta-t.
the change in velocity V over a period of time T.
Delta means "change in"...not period of
just kidding. it all works mathematically
except doesn't time really only change if the instantaneous speeds vary...?
and I assume we are all talking average acceleration
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the rate of change of velocity is callaed acceleration
a=delta v/delta t
the rate of change in velocity with respect to time is acceleration
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what is meant by lost volt
Hardeyyemih Reply
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.
What is physics?
Bedabyas Reply
physics is brance science concerned with nature and properties of matter and energy
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.
physics is study of nature and it's law
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Branch of science (study) of matter, motion and energy
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