nuclear physics & electron ball as tics

8/3/2019 Nuclear Physics & Electron Ball as Tics

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UNIT-1

NUCLEAR PHYSICSAND

ELECTRON BALLASTICS


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Inside Atoms:neutrons, protons,electrons

Carbon (C )

Gold (Au)

Atomic number Z=6(number ofprotons)

Mass number A=12(number ofprotons + neutrons)

# electrons = # protons(count them!)

(atom is electrically neutral)

Atomic number Z = 79

Mass number A = 197

#electrons = # protons

(trust me!)


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Structure of atomic nucleus

Three fundamental subatomic particles-electrons, protons, neutrons.

Nucleus comprise of whole mass ofatom.

Electron moves in the space surrounding

the nucleus.


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1amu=1.6605410-27Kg with energy

equivalence=931.49MeV.

PROTONS : 1.007276AMU

NEUTRONS : 1.008665AMU

ELECTRONS : 0.0005486AMU


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CLASSIFICATION OF ATOMS

ISOTOPES

ISOTONES

ISOBARS

MIRROR NUCLEI


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STATIC PROPERTY OF NUCLEUS

1. Nuclear mass:- it includes the mass of proton& mass of neutron.

Nuclear mass =

But real mass 1 (super-critical mass): starting with one freeneutron, there is a non-trivial probability that isdoes not cause a fission or that a beginning chainreaction dies out.

Generalcondition for self sustained chain reaction


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Critical size


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Nuclear Fission

most stable nuclei atA=60 fission of heavy nuclei

yields energy gain

Weizscker-formula: deformation leads toincrease of surfaceenergy, but to decreaseof Coulomb energy

spontaneous fission for

in general via tunneleffect

Z2

A" 51

N l Fi i P R


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Nuclear Fission Power Reactor

A nuclear power plant resembles a conventionalcoal- or gas-burning power plant, except thatnuclear reactions replace chemical reactions asthe source of heat to generate steam.


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Components of nuclear reactor

1. Reactor core

2. Reactor reflector

3. Moderator4. coolant

5. reactor control material

6. Reactor sheilding


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Site selection of nuclear reactor

Storage for 10,000 years, (minimum)

Isolation from the Water Table

Arid Climate

Rock of Low Porosity and Permeability

Future Climate Change unlikely to raise water table

Rock Absorbent of spills and Dissipative

Very Low Rate of Surface Erosion

Low Probability of Earthquakes and Volcanoes


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NUCLEAR FUSION

process in which two lighter nucleiare combined to fused together to

form a heavier and a Stablenucleus.


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N l F ( h )


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Nuclear Fusion (joining together)

The lightest elements may join together in afusion reaction to form a heavier element,releasing kinetic energy carried by the products(about1,000,000 times that released in chemicalreactions).

Nuclear fusion reactions involving hydrogen

fuel our sun and the stars.


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Energy released in Nuclear fusion

1H2 + 1H2 2He4

Harnessing Fusion Energy


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Harnessing Fusion Energy

Uncontrolled fusion energy has been achieved in the hydrogen atomic

bomb.

Repulsive electrical forces inhibit nuclei from getting close enough tofuse together in a reactor.

Violent collisions at extremely high temperatures (hundreds of millionsof degrees) are needed to harness fusion as an energy source.

Such conditions require magnetic bottles to hold the ionized fuel awayfrom the reactor walls.

Fusion offers the promise of an almost limitless supply of hydrogen fuelin the oceans, but is the most significant scientific and technicalchallenge that mankind has faced.


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Nuclear fusion in stars

Energy is radiated by the sun at the rate of106joules / sec.

Energy is produced in stars by following twoprocess:-

1. Proton proton cycle

2. Carbon nitrogen cycle (CNO)

Proton-Proton Chain


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Proton-Proton Chain

IN: 6 H, (2 e-)OUT: He, 2 H, 2 Re, 4 K

Effectively 4 H nuclei areconverted into 1 He nucleus and

energy is released.

The CNO Cycle


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The CNO Cycle

In the high temperature condition in the core of the high-massstars, another fusion process (the CNO cycle) can fuse hydrogeninto helium at a much faster rate than the proton-proton cycle.

The heavier elements (carbon, nitrogen, and oxygen) act ascatalysis to speed up the hydrogen fusion process

The net result is the same as the proton-proton chain thecreation of a helium atom and release of energy from fusion offour hydrogen nuclei (protons).

The numbers of carbon, nitrogen, and oxygen remain the samebefore and after the reaction.

Where did the carbon, nitrogen, and oxygen come from?

1H1


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6C12

7N13

6C13

7N14

8O15

7N15 1eo

1H1

2He4

1e0

1H1

1H

CNO CYCLE


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CNO CYCLE

Why does fusion occur in the Suns


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Why o s fus on occur n th Sun score ?

Nuclear fusion heavier nuclei are created bycombining (fusing) lighternuclei.

all nuclei are positively charged

Electromagnetic force

causes nuclei to repel eachother. for fusion, nuclei must be

moving fast to overcome E-Mrepulsion

this requires high

temperatures & pressures When nuclei touch, thenuclear force binds themtogether

Fusion Reactions in Stars


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Fusion Reactions in StarsThere are many fusion reactions happening inthe core of the stars. These reactions are

responsible for producing the heavy elements.

Helium Capture: capture of helium byheavier elements

Heavy element fusion

If we know the condition inside the stars, we

can estimate the amount of heavy elements weshould haveand check them withspectroscopy

Th S E S


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The Suns Energy Source

the Sun generates energy via nuclear fusion reactions

Hydrogen is converted into Helium in the Suns core

the mass lost in this conversion is transformed into

energy

the amount of energy is given by Einsteins equation: E= mc2

given the Suns mass, this will provide enough energyfor the Sun to shine for 10 billion years


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11

Institute

ofPhysics

Pe terK a

lm us

Pa rtic

les a

ndth e U

niv erse

Neutrinos

Antiparticles

1950s, 1960s

> 200 new elementary (?) particles

Feel weak forcepredicted p later discovered100,000,000,000,000 per second pass

through each person from the Sun

Equal and opposite properties

predicted p later discoveredAnnihilate with normal particles

Now used in PET scans

Many new particles created

in high energy collisions

Convert energy to mass. Einstein E = mc2


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mx 10101

mx15

101

mx 15107.0

mx18

107.0 e

Thomson (1897): Discovers electron


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Y0001

6028

6027 p eNiCo

Q = -1e almost all trapped in atoms

Q= 0 all freely moving through universe

_


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Just as the equation x2=4 can have twopossible solutions (x=2 OR x=-2), so

Dirac's equation could have twosolutions, one for an electron withpositive energy, and one for an electronwith negative energy.

Dirac interpreted this to mean that forevery particle that exists there is acorresponding antiparticle, exactlymatching the particle but with opposite

charge. For the electron, for instance,there should be an "antielectron" calledthe positron identical in every way butwith a positive electric charge.


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1928 Dirac predicted existence of antimatter

1932 antie

le

ctrons (positrons)

fo

und inconversion of energy into matter

1995 antihydrogen consisting of antiprotons andpositrons produced at CERN

p eeK

In principle an antiworld can be built fromantimatterProduced only in accelerators andin cosmic rays


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p eeraysK


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hfee 2p


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3

1!Q

3

2!Q

1!Q

0!Q


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James Joyce

Murray Gell-Mann


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3

1

3

1

31

3

2

3

2

32


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12

Todays bu ild ing b locks

Lep tons(do not fee l s trong fo rce )

e lectron e - -1

e-neu trino Re 0

Q ua rks(fee l strong fo rce )

up u +2/3

down d -1/3

proton = u u d+2/3 +2/3 -1/3 = +1

neu tron = u d d+2/3 -1/3 -1/3 = 0

4 pa rtic les very s im p le

m ultip ly by 3 (generations )

m ultip ly by 2 (an tipa rtic les )

F irst generation

13

1

3

2

3

2!

03

1

3

1

3

2!

3

2

3

1

Motion in electric and magnetic fields


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For single particle, with no radiation losses and no spacecharge effects:

There are many possibilities, depending on existence andtime-dependence of . For example, if there is nomagnetic field and a time-independent electric field alongthe z-axis, then electrostatic accelerator. If the electricfield is time-dependent, then Linac.

If

= cyclotron frequency.

If = radius of curvature, then

(Lorentz))( BEq

dt

pdv! Y

BE and

m

qBBBBE z

zr!!B!!! U[Y

U

withmotioncircularthenand0and0

m][[T]300MeV/c]in[or VV zz BpqBp !!

Motion in electric and magnetic fields


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g

Some other possibilities listed below:

Accelerator B

Cyclotron Fixed Fixed Variable

Synchrocyclotron Variable Fixed Variable

Synchrotron Variable Variable

Fixed

Orbital accelerators


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As wording implies, focusing in these machines is

weak and, in the early versions, the pole gaps inthe magnets were very large.

Strong focusing dispenses with the requirementof n


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y As mentioned earlier, this is a constant frequency orbital

accelerator, but one in which the orbit radius increases. Frequencygiven by:

Correct for low energies, but as mass increases, orbitalfrequency changes and resonance condition is no longer fulfilled. Toovercome this, either:i. modulate the frequency synchrocyclotron

orii. allow Bz to increase with R, to keep =const. Now n


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Principle of operation: This is a constant radius acceleratorwhere both the frequency and the magnetic field vary withtime in order to maintain the synchronism condition.

Now and it is easy to showthat:

Therefore, angular frequency increases at B-dependentrate, initially fast but then more and more slowly, as >>1.

Energy range for p beams:

Conventional magnets give fields of up to 2T. There is a min.

field of about 10-2

T, hence Emin5x10

-3

Emax Hence, the beam has to be injected with Emin, which is

provided by a linac or another synchrotron (booster) or alinac-booster combination.

Superconducting magnets provide Bmax8T and Bmin=?

2/1

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0

222

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cm

RBqm

qB

![

3

0

3

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andK

[

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m

q

Bm

Bq

R

!

x

x!

Synchrotrons


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Energy range for (e-,e+) beams:

At medium energies, previous comments apply.

Above about 10GeV, SR loss is severe. Accelerator costoptimization requires that maximum machine radiusRmax(Emax)2. Hence, Bmax 1/Emax. Typically, LEP had Bmax0.1T.

Synchrotrons do not need a continuous magnet around theorbit but operate with a ring of magnets. Therefore, theyhave achieved major savings in the magnet iron. They are themain machine for high energy physics.

A note on synchrotron radiation


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Accelerated charges emit radiation whose power (P) is givenby:

For linear motion,

For a linear accelerator dE/dx must be of the order of 1014

MeV/m before this becomes significant compared to powersupplied by external sources.

For circular machines

? A 1898)(Lienard,)(.32 26

2

FFFFK

v! c

e

P

2

32

0

2

2

32

0

2

3

0

)(3

2)(

3

2

hence,1

and0

dx

dE

cm

e

dt

dp

cm

eP

dt

pd

cmdt

d

!!

!!vK

FFF

term.extraNote

radius.where,3

2

3

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44

2222

32

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K

VKFV

[K !!!ce

pcm

eP

Synchrotron radiation


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For , the energy lost per turn has a numerical valuegiven by:

Some numbers: for LEP at 86GeV, 1.37GeV/electron;there are about 6x1012 electrons/beam, hence power lost is20MW; power needed for RF is about 96MW.

SR was originally perceived as a nuisance; now it is a fieldwith many important applications, with large, dedicatedaccelerators (ESRF at Grenoble, ALS at Brookhaven,DIAMOND at RAL etc).

m)inGeV,in(,1085.8)MeV(4

2 V

V

H EE

xE

!

CYCLOTRON


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CYCLOTRONPrinciple:-The cyclotron was one of the

earliest types of particle accelerators, Itmakes use of the magnetic force on amoving charge to bend moving chargesinto a semicircular path between

accelerations by an applied electric field.The applied electric field accelerateselectrons between the "dees" of themagnetic field region. The field isreversed at the cyclotron frequency toaccelerate the electrons back across thegap.


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CYCLOTRON FREQUENCY


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CYCLOTRON FREQUENCY

A moving charge in a cyclotron will move in acircular path under the influence of aconstant magnetic field. If the time tocomplete one orbit is calculated:

it is found that the period is independent of

the radius. Therefore if a square wave isapplied at angular frequency qB/m, the chargewill spiral outward, increasing in speed

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When a square wave of angular


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When a square wave of angularfrequency

is applied between the two sides of

the magnetic poles, the charge will beboosted again at just the right timeto accelerate it across the gap. Thusthe constant cyclotron frequency can

continue to accelerate the charge (solong as it is not relativistic).

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BAINBRIDGEMASSSPECTROGRAPH


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