Nuclear Physics What’s Inside… In this module, we discuss the properties and structures of atomic nucleus. We start by describing the basic properties.

Nuclear PhysicsNuclear Physics

What’s Inside…What’s Inside…

In this module, we discuss the properties In this module, we discuss the properties and structures of atomic nucleus. We start and structures of atomic nucleus. We start by describing the basic properties of the by describing the basic properties of the nuclei and then the discussion of nuclear nuclei and then the discussion of nuclear forces and binding energy, and the forces and binding energy, and the phenomenon of radioactivity. After that we phenomenon of radioactivity. After that we tackle about nuclear reaction and the tackle about nuclear reaction and the various processes by which nuclear various processes by which nuclear decay. By the way, we’ll also talk about decay. By the way, we’ll also talk about fusion reaction. ^^fusion reaction. ^^

Table of Contents….Table of Contents….

I.I. Introductions……………….........................................….1-3Introductions……………….........................................….1-3II.II. Pre-Test……………………………...................................4-13Pre-Test……………………………...................................4-13III.III. The Nucleus……………………………………………......14-19The Nucleus……………………………………………......14-19IV.IV. Quiz 1………………………………………………………..20-25Quiz 1………………………………………………………..20-25V.V. Binding energy and Nuclear stability……………………..26-33Binding energy and Nuclear stability……………………..26-33VI.VI. Quiz 2………………………………………………………..34-38Quiz 2………………………………………………………..34-38VII.VII. Radioactive Decay and Half-life…………………………..39-57Radioactive Decay and Half-life…………………………..39-57VIII.VIII. Quiz 3…………………………………………………….….58-63Quiz 3…………………………………………………….….58-63IX.IX. Nuclear Reaction…………………………………………...64-70Nuclear Reaction…………………………………………...64-70X.X. Quiz 4………………………………………………………..71-75Quiz 4………………………………………………………..71-75XI.XI. Fusion Reaction…………………………………………….76-85Fusion Reaction…………………………………………….76-85XII.XII. Quiz 5……………………………………………………......86-87Quiz 5……………………………………………………......86-87XIII.XIII. Post test……………………………………………………..88-99Post test……………………………………………………..88-99XIV.XIV. Answers……………………………………………………..100-107Answers……………………………………………………..100-107

Pre-testPre-test

Let’s see what you’ve got….Let’s see what you’ve got….

1.1. Which of the following is not an example Which of the following is not an example of ionizing radiation? of ionizing radiation?

a. alphaa. alpha

b. betab. beta

c. gammac. gamma

d. x-rayd. x-ray

e. microwavee. microwave

2.2. What is the atomic number of  ?What is the atomic number of  ?

3.3. In beta decay, β–, an electron is emitted In beta decay, β–, an electron is emitted along with the daughter nucleus. What is along with the daughter nucleus. What is the other particle emitted?the other particle emitted?

4.4. emits a gamma ray. The resulting emits a gamma ray. The resulting nucleus isnucleus is

23692U

22890Th

5.5. Uranium-236 fissions into and Uranium-236 fissions into and another nucleus with the release of three another nucleus with the release of three neutrons. What is the atomic mass neutrons. What is the atomic mass number of the second nucleus? number of the second nucleus?

6.6. decays by alpha decay. The decays by alpha decay. The resulting isotope isresulting isotope is

13858 X

21084Po

7.7. An amateur scientist tells you he has a An amateur scientist tells you he has a stable atom of , why is that stable atom of , why is that unlikely?unlikely?a. No atoms are stable a. No atoms are stable b. Amateur scientists don't know b. Amateur scientists don't know

anything. anything. c. There are no stable nuclei with more c. There are no stable nuclei with more than 83 protons. than 83 protons. d. Male scientists can't be trusted. d. Male scientists can't be trusted.

21284Po

8.8. An alpha particle is An alpha particle is

a. an electron a. an electron

b. a positron b. a positron

c. a Helium nucleus c. a Helium nucleus

d. the first one to come out d. the first one to come out

9.9. A beta particle is A beta particle is

a. an electron a. an electron

b. a positron b. a positron

c. a Helium nucleus c. a Helium nucleus

d. the second to come out d. the second to come out

10.10. A gamma ray is A gamma ray is

a. an electron a. an electron

b. a Helium nucleus b. a Helium nucleus

c. an energetic ray of invisible light  c. an energetic ray of invisible light 

d. the 3rd to come out d. the 3rd to come out

11.11. A hypothetical stable nucleus with 89 A hypothetical stable nucleus with 89 protons and 129 neutrons must have a protons and 129 neutrons must have a mass of less than __ u (to the nearest mass of less than __ u (to the nearest ten thousandth of a u). ten thousandth of a u).

12. element has the same Z values but differ in N and A values

13.13. What is the mass of to the nearest u?What is the mass of to the nearest u?

14.14. The strongest force in natureThe strongest force in nature

15.15. who first observe nuclear reactions?who first observe nuclear reactions?

23292U

The NucleusThe Nucleus

Chapter IChapter I

Atomic NumberAtomic Number equal to the number of protonequal to the number of proton

Neutron NumberNeutron Number equal to the number of neutronequal to the number of neutron

Mass NumberMass Number equal to the number of equal to the number of nucleonnucleon

↖↖[proton + neutron][proton + neutron]

We describe the atomic nucleus We describe the atomic nucleus using the following quantities…..using the following quantities…..

In representing the nuclei we use this symbol:

X NZ

A

Atomic Number

Mass Number

Element

fortunately, neutron number usage is obsolete so it’s not necessary to include that in writing the element

NeutronNumber

The isotopes of an element has the same Z values but differ in N and A values

Isobars are elements with the same mass number A but different Z

isotones are elements with the same number of neutrons N which are relatively rare

The Mass and ChargeThe Mass and ChargeCHARGECHARGE MASSMASS

cc KgKg UU MeV/cMeV/c22

ProtonProton1.6x101.6x10-19-19 1.67262x101.67262x10-27-27 1.0072761.007276 938.28938.28

NeutronNeutron00 1.67493x101.67493x10-27-27 1.0086651.008665 939.57939.57

ElectronElectron-1.6x10-1.6x10-19-19 9.10939x109.10939x10-31-31 5.48579x105.48579x10-4-4 0.5109990.510999

Coloumb (c)Unified Atomic Mass Unit (u),u ≈ 1.66053886 × 10−27 kg ≈ 931.49 MeV/c2

The Size and Structure of the The Size and Structure of the NucleiNuclei

The radius of a nucleon is of the order of 1 fermi = 10-15 m

The nuclear radius can be approximated by:The nuclear radius can be approximated by:

1

30R R A

Mass Number

1.2 fm

The nucleus is viewed as a closely packed collection of protons and neutrons

The volume of the The volume of the nucleus (assumed to be nucleus (assumed to be spherical) is directly spherical) is directly proportional to the total proportional to the total numbers of nucleonnumbers of nucleon

This suggest that all This suggest that all nuclei have nearly the nuclei have nearly the same densitysame density

Quiz # 1Quiz # 1

Quiz # 1Quiz # 1

1.1. The mass number of a nuclide refers to the The mass number of a nuclide refers to the sum of the masses of _____.sum of the masses of _____.

a. the protons and neutrons in the a. the protons and neutrons in the nucleus nucleus

b. the protons in the nucleus b. the protons in the nucleus

c. the electrons in the nucleus c. the electrons in the nucleus

d. the neutrons in the nucleus d. the neutrons in the nucleus

Quiz # 1Quiz # 1

2.2. Which one of the nuclides shown below Which one of the nuclides shown below is an isotope of is an isotope of

a.a.

b.b.

c.c.

d.d.

Quiz # 1Quiz # 1

3.3. Which one of the nuclides shown below has the same Which one of the nuclides shown below has the same number of neutrons as the number of neutrons as the nuclide nuclide

a.a.

b.b.

c.c.

d.d.

Quiz # 1Quiz # 1

3.3. Isotones are elements with….Isotones are elements with….

a. a. the same mass number A but different Z

b. b. the same Z values but differ in N and A values

c. the same number of N but differ in Z and A but differ in Z and A valuesvalues

d. the same number of A,N and Z valuesd. the same number of A,N and Z values

Quiz # 1Quiz # 1

5.5. It is the number of protons and neutronsIt is the number of protons and neutrons

a. nuclidea. nuclide

b. neutrinob. neutrino

c. nucleonc. nucleon

d. nucleotidesd. nucleotides

Binding Energy and Binding Energy and Nuclear Stability Nuclear Stability

Chapter IIChapter II

Binding Energy and Nuclear Binding Energy and Nuclear StabilityStability

The nuclei are stable because of the The nuclei are stable because of the strong strong nuclear forcenuclear force

It is the competition between the repulsive It is the competition between the repulsive electrostatic forceselectrostatic forces and the attractive and the attractive strong nuclear forcesstrong nuclear forces that determines that determines whether a given nucleus is stablewhether a given nucleus is stable

Nuclear forceNuclear force

a very short range (about 2 fm) attractive a very short range (about 2 fm) attractive force that acts between all nuclear force that acts between all nuclear particlesparticles

it acts between pairs of neutrons and it acts between pairs of neutrons and between neutrons and protonsbetween neutrons and protons

The strongest force in natureThe strongest force in nature Independent of the charge of interactive Independent of the charge of interactive

nucleonsnucleons

Proton Count (Z)

Neu

tron

Cou

nt (

N)

Here, we plotted N vs. Z for a number of stable nuclei (black dots)

This is the line of

stability

N=Z

light nuclei are most stable if they contain an equal number of Z and N

heavy nuclei (Z>20) are more stable if Z is greater than N

Elements which have Z>83 doesn’t have stable nuclei

The mass of a nucleus is always less than the The mass of a nucleus is always less than the sum of the masses of its constituent nucleons. sum of the masses of its constituent nucleons.

The difference is known as The difference is known as mass defectmass defect::

ΔΔm is the mass that would be transformed into m is the mass that would be transformed into energy, if a nucleus is to be constructed by the energy, if a nucleus is to be constructed by the necessary number of protons and neutrons.necessary number of protons and neutrons.

,p nm Zm Nm m Z A Mass

of proton Mass of

neutronMass of

the nucleus

The energy equivalent of the mass defect The energy equivalent of the mass defect is called the is called the binding energybinding energy of the nucleusof the nucleus

Binding energy (EBinding energy (Ebb)) energy needed to split a nucleus into its energy needed to split a nucleus into its

componentscomponents energy needed to bind the nucleienergy needed to bind the nuclei

931.494 /b p n AE MeV Zm Nm M MeV u

*the masses are all expressed in atomic mass units

MASS NUMBER

BIN

DIN

G E

NE

RG

Y P

ER

NU

CLE

ON

(M

eV)

Binding energy of the nucleon vs. mass number for nuclei that lie along the line of stability

Nuclei having A > or < 60 are not as strongly bound as those near in the middle periodic table

as the atomic mass number increases, the binding energy per nucleon decreases for A > 60

binding energy per nucleon is approximately constant at around 8 MeV per nucleon for all nuclei with A>50

Region w/ greatest stability

The lightest nuclei, like deuterium and tritium, have the The lightest nuclei, like deuterium and tritium, have the smallest binding energy smallest binding energy

Iron-56 is the most tightly bound nucleus Iron-56 is the most tightly bound nucleus

The heaviest nuclei are not bound as loosely as the The heaviest nuclei are not bound as loosely as the lightest nuclei, but are bound less tightly than those with lightest nuclei, but are bound less tightly than those with A =60 A =60

Fusion is the process of bringing together two light nuclei Fusion is the process of bringing together two light nuclei to form a more tightly bound heavier nucleus while to form a more tightly bound heavier nucleus while releasing a particle...typically a neutron. releasing a particle...typically a neutron.

Fission is a process in which a heavy nucleus fragments Fission is a process in which a heavy nucleus fragments into two medium nuclei with the release of two or more into two medium nuclei with the release of two or more neutrons neutrons

Quiz # 2Quiz # 2

Quiz # 2Quiz # 2

1-2.1-2. Most stable nuclei with small atomic numbers Most stable nuclei with small atomic numbers have have ____, while those with large atomic numbers have ____, while those with large atomic numbers have

____.____.

a. more neutrons than protonsa. more neutrons than protons

b. more protons than neutronsb. more protons than neutrons

c. equal numbers of neutrons and protonsc. equal numbers of neutrons and protons

d. equal numbers of protons and electronsd. equal numbers of protons and electrons

Quiz # 2Quiz # 2

3.3. Which nuclei have the largest average Which nuclei have the largest average binding energies per nucleon?binding energies per nucleon?

a. A < 20a. A < 20

b. 30 <A< 100b. 30 <A< 100

c. A>200c. A>200

d. they are all the samed. they are all the same

Quiz # 2Quiz # 2

4.4. Which of the following is not true?Which of the following is not true?

a. nuclides located in the middle of the periodica. nuclides located in the middle of the periodic table have greater stability than the otherstable have greater stability than the others

b. b. as the atomic mass number increases, the binding energy per nucleon decreases for A > 60

c. c. binding energy per nucleon is approximately constant at around 8 MeV per nucleon for all nuclei

d. Iron-56 is the most tightly bound nucleus d. Iron-56 is the most tightly bound nucleus

Quiz # 2Quiz # 2

5.5. Nuclear fission Nuclear fission

a. is the splitting of heavy nuclei into lighter onesa. is the splitting of heavy nuclei into lighter ones

b. is the combining of light nuclei to form heavier ones.b. is the combining of light nuclei to form heavier ones.

c. results from a series of alpha decays.c. results from a series of alpha decays.

d. releases much less energy per atom than a d. releases much less energy per atom than a chemical process.chemical process.

Radioactive Decay and Radioactive Decay and Half LifeHalf Life

Chapter IIIChapter III

Radioactivity Radioactivity - the process of - the process of spontaneous emission of radiationspontaneous emission of radiation

Radioactive (unstable) nuclei decay if Radioactive (unstable) nuclei decay if there is an energetically more favorable there is an energetically more favorable condition that it is trying to reachcondition that it is trying to reach

Radioactive DecaysRadioactive Decays Change into another element:Change into another element: [X[XY+decay particle(s)]Y+decay particle(s)]

αα-decay:-decay: emits emits 44He nucleus from unstable He nucleus from unstable nucleusnucleus

ββ-decay:-decay: emission of electron or positron emission of electron or positron (positively charged electron) from (positively charged electron) from unstable nucleusunstable nucleus

Spontaneous fission:Spontaneous fission: the radiocative nucleus the radiocative nucleus brake into so called brake into so called “fission fragments”“fission fragments”

An another decay mode (within the nucleus):An another decay mode (within the nucleus): [X* [X* X + X + γγ’s]’s]

γγ-decay:-decay: De-excitation from 1 excited state to a De-excitation from 1 excited state to a bound state (or less excited one...)bound state (or less excited one...)

α

β

γ

ALUMINUMPAPER LEAD

The rate at which a particular decay process occur in a radioactive The rate at which a particular decay process occur in a radioactive sample is proportional to the number of the radioactive nuclei sample is proportional to the number of the radioactive nuclei present (the ones that haven’t decayed yet…)present (the ones that haven’t decayed yet…)

The rate of change in N (# of radioactive nuclei present) is…..The rate of change in N (# of radioactive nuclei present) is…..

0 or dtdNN N N e

N

Decay Constant -the probability of decay per nucleus per second

* The minus sign indicates that N decreases in time

The number of radioactive nuclei at t=0

The decay rate which is the number of decays per The decay rate which is the number of decays per second can be obtained by differentiating the latter second can be obtained by differentiating the latter equation (rate of change) with respect to time.equation (rate of change) with respect to time.

The decay rate R of a sample is often referred to as it’s The decay rate R of a sample is often referred to as it’s activityactivity

0 0

0 0where and

is the decay rate at 0

t tdNR N e R e

dt

R N R N

t

Half-lifeHalf-life The time it takes half of a given number of radioactive The time it takes half of a given number of radioactive

nuclei to decaynuclei to decay This is a convenient relating half-life to decay constantThis is a convenient relating half-life to decay constant

The SI unit of activity is The SI unit of activity is BecquerelBecquerel (Bq) (Bq) 1 Bq=1decay/s1 Bq=1decay/s

Another frequently used unit is Another frequently used unit is CurieCurie (Ci) (Ci) 1 Ci=3.7x101 Ci=3.7x101010 decay/s decay/s

1

2

ln 2 0.693T

The half life formula isThe half life formula is

0

1

2

n

N N

The amount of remaining

nuclei

Amount of nuclei at

t=0

Number of half lives

To compute for n

1

2

tn

T

Total time

Time per half life

Alpha DecayAlpha Decay

When a nucleus emits an alpha particle it looses When a nucleus emits an alpha particle it looses 2 protons and 2 neutrons2 protons and 2 neutrons N decreases by 2N decreases by 2 Z decreases by 2Z decreases by 2 A decreases by 4A decreases by 4

Symbolically: Symbolically:

X is call the parent nucleusX is call the parent nucleus Y is called the daughter nucleusY is called the daughter nucleus

4 42 2

A AZ ZX Y He

ExampleExample

Decay of Decay of 226226RaRa

Half life for this decay is Half life for this decay is 1600 years1600 years

Excess mass is Excess mass is converted into kinetic converted into kinetic energyenergy

Momentum of two Momentum of two particles is equal and particles is equal and opposite opposite

226 222 488 86 2Ra Rn He

α-decay

Beta Decay - Electron EnergyBeta Decay - Electron Energy The energy released in the decay The energy released in the decay

process should process should almost allalmost all go to go to the kinetic energy of the electronthe kinetic energy of the electron

Experiments show that Experiments show that few few electrons had his amount of electrons had his amount of kinetic energykinetic energy

To account for the “missing” To account for the “missing” energy, in 1930 Pauli proposed energy, in 1930 Pauli proposed the existence of another particlethe existence of another particle

Enrico Fermi later named this Enrico Fermi later named this particle the particle the neutrinoneutrino

Properties of neutrinoProperties of neutrino 0 charge0 charge Mass much smaller than Mass much smaller than

electron, probably not 0electron, probably not 0 Spin of ½ Spin of ½ Very weak interaction with Very weak interaction with

mattermatter

Beta DecayBeta Decay

During beta decay, During beta decay, the daughter nucleus has the the daughter nucleus has the same the daughter nucleus has the same same the daughter nucleus has the same number of nucleons as the parent, but the number of nucleons as the parent, but the atomic number of nucleons is one lessatomic number of nucleons is one less

In addition, an electron (positron) was observedIn addition, an electron (positron) was observed The emission of the electron is from the nucleusThe emission of the electron is from the nucleus

The nucleus contains protons and neutrons The nucleus contains protons and neutrons The process occurs when a neutron is transformed The process occurs when a neutron is transformed

into a proton and an electron and an electroninto a proton and an electron and an electron Energy must be conservedEnergy must be conserved

In beta decay the following pairs are emittedIn beta decay the following pairs are emitted electron and antineutrinoelectron and antineutrino positron and neutrinopositron and neutrino

A positron decay is always followed by A positron decay is always followed by electron capture decayelectron capture decay

Electron capture decayElectron capture decay This occurs when a parent nucleus captures one of This occurs when a parent nucleus captures one of

its own orbital electron and emits a neutrinoits own orbital electron and emits a neutrino

1

1

A AZ Z

A AZ Z

X Y e v

X Y e v

β+ decay

β- decay

01 1

A AZ ZX e Y v

β- decay

β+ decay

Electron capture decay

Gamma DecayGamma Decay Gamma rays are given off when an excited nucleus Gamma rays Gamma rays are given off when an excited nucleus Gamma rays

are given off when an excited nucleus “fall” to a lower energy stateare given off when an excited nucleus “fall” to a lower energy state Similar to the process of electron “jumps” to lower energy states and Similar to the process of electron “jumps” to lower energy states and

giving off photonsgiving off photons The excited nuclear states result from “jumps” made by a proton or The excited nuclear states result from “jumps” made by a proton or

neutron neutron The excited nuclear states may be the result of violent collision of an The excited nuclear states may be the result of violent collision of an

most likely alpha or beta emissionmost likely alpha or beta emission likely of an alpha or beta emissionlikely of an alpha or beta emission Example of a decay sequence

The first decay is a beta emission The second step is a gamma emission

C* indicates that Carbon nucleus is in excited stateC* indicates that Carbon nucleus is in excited state Gamma emission doesn’t change either A or ZGamma emission doesn’t change either A or Z

12 125 6

12 126 6

*

*

B C e v

C C

Gamma Decay

Quiz # 3Quiz # 3

1.1. What is the mass of the daughter What is the mass of the daughter nuclide produced by the nuclear nuclide produced by the nuclear reaction shown below?reaction shown below?

2.2. What is the atomic number, Z, of the What is the atomic number, Z, of the daughter nuclide produced by the daughter nuclide produced by the

nuclear reaction shown below? nuclear reaction shown below?

3.3. Which of the types of radiation below Which of the types of radiation below is is a wave? a wave?

a. alphaa. alpha

b. betab. beta

c. gammac. gamma

4.4. What happens to the atomic number and atomic What happens to the atomic number and atomic mass of an element after it decays by gamma mass of an element after it decays by gamma

radiation? radiation?

a. The atomic number decreases and the mass number a. The atomic number decreases and the mass number increases. increases.

b. The atomic number increases and the mass number b. The atomic number increases and the mass number remains the same. remains the same.

c. The atomic number remains the same and the mass c. The atomic number remains the same and the mass number decreases. number decreases.

d. Both numbers stay the same. d. Both numbers stay the same.

5.5. What is the charge of a neutrino?What is the charge of a neutrino?

a. +a. +

b. –b. –

c. 0c. 0

Nuclear ReactionNuclear Reaction

Chapter IVChapter IV

Nuclear ReactionNuclear Reaction

Collisions that change the identity of the Collisions that change the identity of the target nucleitarget nuclei

Rutherford was the first to observe themRutherford was the first to observe them

Energy, momentum, total charge and total Energy, momentum, total charge and total number of nucleons are conservednumber of nucleons are conserved

Consider a reaction in which a target nucleus X Consider a reaction in which a target nucleus X is bombarded by a particle a, resulting in a is bombarded by a particle a, resulting in a daughter nucleus Y and a particle b.daughter nucleus Y and a particle b.

If a=If a=γγ reaction is called: reaction is called: radiative captureradiative capture If b=If b=γγ reaction is called: reaction is called: nuclear photoeffectnuclear photoeffect

or

,

a X Y b

X a b Y

Nuclear ReactionNuclear Reaction

Reaction EnergyReaction Energy QQ is total energy released at the end of is total energy released at the end of the reactionthe reaction

The energy required to balance a nuclear reaction is The energy required to balance a nuclear reaction is called the called the Q valueQ value of the reaction of the reaction

Exothermic reactionExothermic reaction reaction that have positive Qreaction that have positive Q There is a lost of “mass”There is a lost of “mass” There is a release of energyThere is a release of energy

Endothermic reactionEndothermic reaction There is a gain of “mass”There is a gain of “mass” reaction that have negative Qreaction that have negative Q cannot occur unless the incoming particle has at least enough cannot occur unless the incoming particle has at least enough

kinetic energy to overcome the energy deficit kinetic energy to overcome the energy deficit

2a x y bQ m m m m c

Determine the product of the reactionDetermine the product of the reaction What is the Q value?What is the Q value? In order to balance the reaction, the total amount of nucleons (sum

of A-numbers) must be the same on both sides. Same for the Z-number.

Thus, it is B…

The Q value is then

ExampleExample7 43 2 ?Li He n

Scattering eventScattering event particle a and b in a nuclear are identical, so particle a and b in a nuclear are identical, so

that X and Y are also necessarily identicalthat X and Y are also necessarily identical Elastic scatteringElastic scattering

Kinetic energy is conserve as a result of the Kinetic energy is conserve as a result of the nuclear reaction (that is, Q=0)nuclear reaction (that is, Q=0)

Inelastic scatteringInelastic scattering Kinetic energy is not conserved (Q≠0)Kinetic energy is not conserved (Q≠0)

Threshold energyThreshold energy minimum kinetic energy necessary for a minimum kinetic energy necessary for a

endothermic reactionendothermic reaction It is determined by:It is determined by:

min 1m

KE QM

Mass of the incident particle

Mass of the target atom

Quiz # 4Quiz # 4

1.1. The energy required to balance a The energy required to balance a nuclear reactionnuclear reaction

2.2. If the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be

a. equal to 2.17 MeV

b. greater than 2.17 MeV

c. less than 2.17 MeV,

d. precisely half of 2.17 MeV.

3. Which of the following are possible reactions?

1 235 140 94 10 92 54 38 0

1 235 132 101 10 92 50 42 0

1 293 127 93 10 94 5 41 0

(a) 2

(b) 3

(c) 3

n U Xe Sr n

n U Sn Mo n

n Pu I Nb n

4.4. It is the minimum kinetic energy It is the minimum kinetic energy necessary for endothermic reactionnecessary for endothermic reaction

5.5. Determine the product of the reactionDetermine the product of the reaction

1 19 41 9 2?H F He

Fusion ReactionFusion Reaction

Chapter VChapter V

Nuclear FusionNuclear Fusion

2 light nuclear combine to form heavy nucleus2 light nuclear combine to form heavy nucleus There is a loss of mass accompanied by a There is a loss of mass accompanied by a

release of energyrelease of energy extremely high energies are needed to fuse the extremely high energies are needed to fuse the

nuclei together. This is needed to overcome the nuclei together. This is needed to overcome the electrical repulsion (also known as the coulomb electrical repulsion (also known as the coulomb barrier) between two positively charged nuclei, barrier) between two positively charged nuclei, so that they get close enough to have the strong so that they get close enough to have the strong nuclear force bind the nuclei nuclear force bind the nuclei

Nuclear Fusion

Proton-Proton FusionProton-Proton Fusion The nuclear fusion process that fuels the Sun The nuclear fusion process that fuels the Sun

and other stars which have core temperatures and other stars which have core temperatures less than 15 million Kelvin. A reaction cycle less than 15 million Kelvin. A reaction cycle yields about 25 MeV of energy.yields about 25 MeV of energy.

The fusion of hydrogen in lower temperature The fusion of hydrogen in lower temperature stars like our Sun involve the following reactions stars like our Sun involve the following reactions yielding positrons, neutrinos, and gamma rays. yielding positrons, neutrinos, and gamma rays.

Now let’s see the step by step Now let’s see the step by step process of it…….process of it…….

+

N

NN

N N

N

e+O

Ov

1. Protons fuse

2. One proton is transmuted to a neutron forming deuterium releasing a positron and a neutrino

3. Deuterium fuses with another proton

4. Two of the resulting helium nuclei fuse

5. An alpha particle forms with the energetic release of two protons to complete the process

Symbolically:Symbolically:

1 1 2 01 1 1 1

1 2 31 1 2

1 3 4 01 2 2 1

3 3 4 1 12 2 2 1 1

which can be followed by either

o r

H H H e v

H H He

H He He e v

He He He H H

CNO cycleCNO cycle The CNO cycle is another sequence of energy The CNO cycle is another sequence of energy

producing reactions, which ultimately results in producing reactions, which ultimately results in the conversion of hydrogen to helium. It occurs the conversion of hydrogen to helium. It occurs in stars at temperatures greater than 16 million Kin stars at temperatures greater than 16 million K

Although hydrogen and helium are the main Although hydrogen and helium are the main elements in stars, usually some heavier elements in stars, usually some heavier elements are present in much smaller quantities elements are present in much smaller quantities

The CNO process was proposed in 1938 by The CNO process was proposed in 1938 by Hans Bethe Hans Bethe

quantities. If Carbon (C), Nitrogen (N), and Oxygen (O) quantities. If Carbon (C), Nitrogen (N), and Oxygen (O) ions are present, they may be involved in the release of ions are present, they may be involved in the release of energy within stars through the following sequence of energy within stars through the following sequence of reactions: reactions:

In the above reactions, Carbon(C) acts as the catalyst, In the above reactions, Carbon(C) acts as the catalyst, that is, it initiated the chain of reactions but was not that is, it initiated the chain of reactions but was not consumed (notice that consumed (notice that 1212C reappears in the last equation)C reappears in the last equation)

12 1 13

13 13

13 1 14

14 1 15

15 15

15 1 12 4

C H N

N C e v

C H N

N H O

O N e v

N H C He

1H

1H

1H

NN

42He

N

N

N

NNNN

158O

N NNN

NN

126C

N NN

NN

N

137N

N

N NN

NNN136C

NN

NN

NN

N

147N

NN

N

NN N

N157N

e

v

e

v

N

proton

neutron

positron

neutrino photon

C-12 acts as a nuclear catalyst

The CNO Cycle 1H

D-T processD-T process 66Li + n ---Li + n --- t + t + 44He + 4.8 MeVHe + 4.8 MeV d + t ----d + t ---- n + n + 44He + 17.6 MeVHe + 17.6 MeV

66Li + d -----Li + d ----- 2( 2(44He) + 22.4 MeVHe) + 22.4 MeV

Since some of the neutrons would escape, Since some of the neutrons would escape, these would merely used up the hard won these would merely used up the hard won initial supply of tritium. Fortunatley natural initial supply of tritium. Fortunatley natural lithium contains more lithium contains more 77Li than Li than 66Li and Li and

77Li + d --------Li + d -------- 66Li + 2nLi + 2n

DisadvantagesDisadvantages

1.1. Extremely expensive to buildExtremely expensive to build

2.2. Extremely radioactive due to production Extremely radioactive due to production of high energy neutronsof high energy neutrons

3.3. A source of thermal pollutionA source of thermal pollution

Quiz # 5Quiz # 5

1.1. Who proposed the CNO cycle?Who proposed the CNO cycle?

2.2. What element acts as a catalyst in the What element acts as a catalyst in the CNO cycle?CNO cycle?

3.3. What is needed to overcome the What is needed to overcome the Coulomb barrier?Coulomb barrier?

4.4. Is photon-photon reaction exothermic?Is photon-photon reaction exothermic?

5.5. TRUE or FALSE: fusion can happen TRUE or FALSE: fusion can happen between heavy nuclei.between heavy nuclei.

Post TestPost Test

Now what did you get….Now what did you get….

1.1. Which types of decay will cause no Which types of decay will cause no decrease in the atomic mass of the decrease in the atomic mass of the nuclei?nuclei?

a. alpha beta and gammaa. alpha beta and gamma

b. beta positron and gammab. beta positron and gamma

c. alpha and gammac. alpha and gamma

d. positron emission onlyd. positron emission only

2.2. In the reaction shown below what particle In the reaction shown below what particle is represented by X?is represented by X?

81 8137 36Rb Kr X

3.3. In the reaction shown below what particle In the reaction shown below what particle is represented by X?is represented by X?

209 20981 82Tl Pb X

4.4. In the reaction shown below what particle In the reaction shown below what particle is represented by X?is represented by X?

212 20884 82Po Pb X

5.5. What kind of decay is shown in this What kind of decay is shown in this equation?equation?

81 0 8137 1 36Rb e Kr

6.6. What is the neutron number of What is the neutron number of

23692U

7.7. Complete the reactionComplete the reaction

3 3 1 12 2 1 1 ?He He H H

8.8. Complete the reactionComplete the reaction

253 14292 57 ?n U n n La

9.9. It is the energy needed to split the It is the energy needed to split the nucleus into it’s components.nucleus into it’s components.

10.10. It is the nuclear fusion process that fuels It is the nuclear fusion process that fuels the sunthe sun

11.11. The carbon-14 activity of a 130-gram The carbon-14 activity of a 130-gram sample of ancient wood has an activity of sample of ancient wood has an activity of 1.04 Bq. To the nearest year, what is its 1.04 Bq. To the nearest year, what is its age? age?

12.12. A nucleus with an atomic mass of A nucleus with an atomic mass of 238.05112, alpha decays into a nucleus 238.05112, alpha decays into a nucleus of mass 234.03391. To the nearest of mass 234.03391. To the nearest hundredth of a MeV, how much energy is hundredth of a MeV, how much energy is released? released?

13.13. To the nearest hundredth of a fermi, To the nearest hundredth of a fermi, what is the radius of uranium- 235? what is the radius of uranium- 235?

14.14. A sample of 1.2 x 10A sample of 1.2 x 1077 nuclei with a decay nuclei with a decay constant of 1.91 x 10constant of 1.91 x 10-5-5/s is left for two /s is left for two days. How many are left? days. How many are left?

15.15. How many neutrons does the nucleus How many neutrons does the nucleus have? have?

23490 X

AnswersAnswers

Pre-TestPre-Test

1.1. EE2.2. 92923.3. AntineutrinoAntineutrino4.4. 5.5. 86866.6. 7.7. CC8.8. CC9.9. A and BA and B

10.10. cc11.11. 212.7536212.753612.12. IsotopesIsotopes13.13. 232 u232 u14.14. Nuclear forceNuclear force15.15. Rutherford Rutherford

22890Th

20682Pb

Quiz # 1Quiz # 1

1.1. AA

2.2. AA

3.3. AA

4.4. CC

5.5. CC

Quiz # 2Quiz # 2

1.1. CC

2.2. AA

3.3. BB

4.4. CC

5.5. AA

Quiz # 3Quiz # 3

1.1. 234234

2.2. 9393

3.3. CC

4.4. DD

5.5. CC

Quiz # 4Quiz # 4

1.1. Q valueQ value

2.2. BB

3.3. A and BA and B

4.4. Threshold energyThreshold energy

5.5. 168O

Quiz # 5Quiz # 5

1.1. Hans BetheHans Bethe

2.2. Carbon 12Carbon 12

3.3. Very high temperatureVery high temperature

4.4. YesYes

5.5. False False

Post-TestPost-Test

1.1. BB

2.2. PositronPositron

3.3. BetaBeta

4.4. AlphaAlpha

5.5. Electron captureElectron capture

6.6. 144144

7.7. . .

8.8. . .

9.9. Binding energyBinding energy

10.10. Photon-photon Photon-photon fusionfusion

11.11. 1655316553

12.12. 12.9812.98

13.13. 7.457.45

14.14. 12015041201504

15.15. 15.14715.147

42He9235Br

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