Topic : Nuclear PhysicsTopic : Nuclear Physics

•Mass excess and nuclear binding energyMass excess and nuclear binding energy•Radioactive decayRadioactive decay

Einstein’s Famous EquationEinstein’s Famous Equation

Mass and Energy are interchangeable!!

Where & When??Where & When??

It happens only at the nuclear levelnuclear level

When two nuclei combine (FusionFusion)

OR When a nucleus breaks up (FissionFission)

Mass ExcessMass Excess

Proton NeutronNucleus

mp mnmnucleus

When protons and neutrons come together to form a nucleus, the mass of the mass of the nucleusnucleus is lessless thanthan the sum of the masses of separated protons and neutronssum of the masses of separated protons and neutrons.

This difference in mass is called the mass excessmass excess or mass defectmass defect of the nucleus.

Mass Excess (Defect)

= Mass of separated protons & neutrons – mass of nucleus

mm = = ZmZmpp + + NmNmpp – – mmnucleusnucleus

Where Z is the number of proton and N the number of neutrons in the nucleus.

Atomic Mass Unit (u)Atomic Mass Unit (u) At nuclear level, the masses of the nuclei and nucleons At nuclear level, the masses of the nuclei and nucleons

are so small that the unit are so small that the unit kgkg is is too bigtoo big and clumsy to be and clumsy to be used.used.

Instead the Instead the atomic mass unitatomic mass unit ( (uu) is used.) is used. One atomic mass unit (One atomic mass unit (1 u1 u) is defined as being equal to ) is defined as being equal to

one-twelfth the mass of a carbon-12 atomone-twelfth the mass of a carbon-12 atom.. 1 u1 u = = 1.66 × 101.66 × 10-27 -27 kgkg Using this scale of measurement, to six decimal places, Using this scale of measurement, to six decimal places,

we havewe haveproton mass, proton mass, mmpp = 1.007276 u = 1.007276 uneutron mass, neutron mass, mmnn = 1.008665 u = 1.008665 uelectron mass, electron mass, mmee = 0.000549 u= 0.000549 u

Example 1Example 1

Calculate the mass defect for a carbon-14 nucleus .Calculate the mass defect for a carbon-14 nucleus .The measured mass is 14.003240 u.The measured mass is 14.003240 u.Calculate also the energy-equivalent of this mass loss in eV.Calculate also the energy-equivalent of this mass loss in eV.

Solution:Solution:Carbon-14 has 6 protons and 8 neutronsCarbon-14 has 6 protons and 8 neutronsMass defect = 6 (1.007276) + 8 (1.008665) –14.003240Mass defect = 6 (1.007276) + 8 (1.008665) –14.003240

= 0.109736 u= 0.109736 u

E E = = mcmc22 = [(0.109736 × 1.66 × 10 = [(0.109736 × 1.66 × 10-27-27) × (3.00 ×10) × (3.00 ×1088))22] /] / ( (1.6 ×101.6 ×10-19-19) ) = 102 MeV = 102 MeV

146C

Binding energyBinding energy

Within the nucleus, there are Within the nucleus, there are strong forcesstrong forces which bind which bind the protons and neutrons together. the protons and neutrons together.

To completely separate all these nucleons To completely separate all these nucleons requires requires energyenergy..

This energy is referred to as the This energy is referred to as the binding energybinding energy.. Binding energyBinding energy is defined as is defined as the energy required to the energy required to

completely separate all nucleons of a nucleuscompletely separate all nucleons of a nucleus.. It is the It is the energy equivalent of the mass defectenergy equivalent of the mass defect of a of a

nucleus.nucleus.

Binding EnergyBinding Energy

When separated nucleons combineWhen separated nucleons combine to to form a nucleus, there is a reduction of form a nucleus, there is a reduction of mass and mass and an equivalent amount of binding an equivalent amount of binding energy is releasedenergy is released..

Binding Energy Per NucleonBinding Energy Per Nucleon

Binding energy per nucleonBinding energy per nucleon is the total binding is the total binding energy of the nucleus divided by the total number energy of the nucleus divided by the total number of nucleons.of nucleons.

Binding energy per nucleonBinding energy per nucleon

= = Binding energy of the nucleus Binding energy of the nucleus J per nucleonJ per nucleon

Nucleon number of the nucleus Nucleon number of the nucleus

It is It is a measure of the stability of the nucleus.a measure of the stability of the nucleus.

Example 2Example 2

Solution 2Solution 2

Example 3Example 3

Solution 3Solution 3

Stability of NucleiStability of Nuclei

The The nucleus is more stablenucleus is more stable if it has a if it has a higher binding energy per nucleonhigher binding energy per nucleon. It . It would be more difficult to break up the nucleus as more energy is required would be more difficult to break up the nucleus as more energy is required to separate the nucleons.to separate the nucleons.

The The most stable nuclidemost stable nuclide can be found at the peak of the curve. It corresponds can be found at the peak of the curve. It corresponds to the element to the element

It has the It has the greatest mass defectgreatest mass defect and the and the highest binding energy per nucleonhighest binding energy per nucleon..

Most stable region

5626 Fe

Mass per NucleonMass per Nucleon

Mass per nucleonMass per nucleon is is smallsmall when when binding energy per nucleonbinding energy per nucleon is is high.high. Elements with Elements with very smallvery small or or very large mass number very large mass number areare unstable unstable.. To attain stabilityTo attain stability

Nuclei with Nuclei with low masslow mass numbers may undergo numbers may undergo nuclear fusionnuclear fusion Nuclei with Nuclei with high masshigh mass numbers may undergo numbers may undergo nuclear fissionnuclear fission..

Nuclear FusionNuclear Fusion Nuclei with Nuclei with low mass numberslow mass numbers may may

undergo nuclear fusionundergo nuclear fusion under certain under certain conditions.conditions.

In general nuclear fusion is possible as In general nuclear fusion is possible as long as the long as the final product has more binding final product has more binding energy per nucleonenergy per nucleon (i.e. less mass) than (i.e. less mass) than the reactants.the reactants.

The enormous amount of The enormous amount of energy energy generated in the Sungenerated in the Sun is due to this is due to this process.process.

Energy releasedEnergy released in the fusion process is in the fusion process is very much greatervery much greater than energy released in than energy released in the fission processthe fission process

An example of nuclear fusion: An example of nuclear fusion: two deuterium atoms fuse together to form two deuterium atoms fuse together to form

helium-3 under extremely high helium-3 under extremely high temperature.temperature.

He-3 has a greater binding energy per He-3 has a greater binding energy per nucleon and is more stable than deuterium.nucleon and is more stable than deuterium.

2 2 3 11 1 2 0H + H He + n + energy

Nuclear FissionNuclear Fission

In general, In general, heavier nuclidesheavier nuclides tend to tend to disintegrate into lighter, more disintegrate into lighter, more stable nucleusstable nucleus..

Fission fragments have a Fission fragments have a greater binding energy per nucleongreater binding energy per nucleon (i.e. less (i.e. less mass per nucleon) than the original nuclide.mass per nucleon) than the original nuclide.

Example: Uranium-235 may absorbs a slow thermal neutron and splits Example: Uranium-235 may absorbs a slow thermal neutron and splits into two part, Xenon-144 and Strontium-90. into two part, Xenon-144 and Strontium-90.

1 235 236 * 144 90 10 92 92 54 38 0n + U U Xe + Sr + 2 n

Example 4Example 4

Solution 4Solution 4

Example 5Example 5

Solution 5Solution 5

Radioactive DecayRadioactive Decay

Radioactive decayRadioactive decay is the is the spontaneousspontaneous and and random disintegrationrandom disintegration of of heavy unstable nucleusheavy unstable nucleus into into more stable products with lower total massmore stable products with lower total mass through the emission of radiation such as through the emission of radiation such as alpha-alpha-particlesparticles, , beta-particlesbeta-particles and and gamma-rays.gamma-rays.

Measuring RadioactivityMeasuring Radioactivity

Radioactivity decay can be measured with a Radioactivity decay can be measured with a Geiger-Muller tubeGeiger-Muller tube connected to a connected to a ratemeterratemeter. The ratemeter measures the count rate of . The ratemeter measures the count rate of the radioactive decaythe radioactive decay

A radiation detector can register a A radiation detector can register a count rate of 20-50 count per count rate of 20-50 count per secondsecond, even in the apparent absence of radioactive materials. This , even in the apparent absence of radioactive materials. This is know as the is know as the background countbackground count. The radiation comes from low . The radiation comes from low intensity radiation from small quantities of radioisotopes found in the intensity radiation from small quantities of radioisotopes found in the ground, atmosphere and cosmic rays arriving at the surface of the ground, atmosphere and cosmic rays arriving at the surface of the Earth.Earth.

Decay ConstantDecay Constant

In a random process, the In a random process, the rate of radioactive decayrate of radioactive decay -d-dNN/d/dtt of a of a radioactive sample is radioactive sample is directly proportionaldirectly proportional to the number to the number NN of of radioactive nucleiradioactive nuclei present. That is,present. That is,

wherewhere

= = radioactivity decay constantradioactivity decay constant; ; t t = time= time

The The decay constant decay constant is the is the fraction of the total number of atoms that fraction of the total number of atoms that decay per unit timedecay per unit time. .

Its S.I. unit is sIts S.I. unit is s-1-1

d

dd

d

NN

tN

Nt

Decay ConstantDecay Constant

The radioactive law The radioactive law ddNN/d/dt t = = NN can be can be rewritten and integrated as follows:rewritten and integrated as follows:

0

0

0

0

0

0

d

dd

d

d

ln

ln

N t

N

N t

N

t

NN

tN

tNN

tN

N t

Nt

N

N N e

In generalIn general x x == x x00 e e--tt

where where xx could representcould represent(a) activity(a) activity AA(b) number of undecayed particles(b) number of undecayed particles NN(c) count rate(c) count rate CC oror(d) mass of undecayed particles(d) mass of undecayed particles mm

ActivityActivity

The activity The activity AA of a radioactive source is the of a radioactive source is the number of disintegration it undergoes per unit number of disintegration it undergoes per unit time.time.

AA == ddN N / d/ dtt = = NN == NN0 0 ee--tt == A A00 ee--tt

Unit of Unit of AA is is becquerelbecquerel, , BqBq

1 Bq1 Bq = = 1 decay s1 decay s-1-1

Graphical RepresentationGraphical Representation

Half LifeHalf LifeThe half-life of a radioactive nuclide is the time taken for the number of radioactive nuclide to disintegrate to half its initial value.

Graph of lnGraph of lnNN against against tt

Half Life of Some MaterialsHalf Life of Some Materials

uranium = 4500 million yearsuranium = 4500 million years radium = 1600 yearsradium = 1600 years polonium = 138 dayspolonium = 138 days radioactive lead = 27 minutesradioactive lead = 27 minutes radon = 1 minuteradon = 1 minute

Example 6Example 6

Solution

Example 7Example 7

Example 8Example 8

Solution 8Solution 8

Example 9Example 9

Solution 9Solution 9

Physics is GreatPhysics is Great

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