Experiment | TheoryDark Matter + Dark Energy | Supersymmetry? Strings?

Nanoscience/Nanotechnology

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RADIOACTIVE DECAY—SOME BASICS(Thornton and Rex, Section 12.6)

At t = 0, N0 radioactive nuclei

Rate of decay = -dN(t)/dt = N(t)

dN(t)/N(t) = - dt

0

t t

o ot t0 0

t /t0 0 0

1 / 2 0 1 / 2 0

IntegratingdN dtN

n N t

N(t ) N (0 )e N (0 )e , with 1 /Or ,when half of number gone,

1 n(1 / 2 ) n(2 )N(t ) N (0 ) t 0.6932

N0(t=0)

N(t)

n p + e- + eDecay scheme

RUTHERFORD SCATTERING:FINAL RESULTS

N() = no. scatteredinto interval to+d

Ni = total no. ofparticles incidentin area A

t = thickness oftarget foil

n = density ofscattering atoms

r = distance ofdetection

K = particle kineticenergy

= distance of closestapproach

Rutherfordformula

0

:1

4

tan

C

B

For convenience

k

Notk Boltzmann

cons t

N = Z

Theory:Outer limitsof nuclearbinding

N = Z

PhysicsToday,Dec. 2004

Stable =Unstableable-too manymany protonsUnstable-too many neutrons

OVERALL POTENTIAL BETWEENTWO NUCLEONS:

proton-protonproton-neutronneutron-neutron

F

“Yukawa meson”really a Pion

dN/dt = -NIntegrate

N = N0at t = 0

The Basic Law of Nuclear Decay:

14 146 7

1 / 2

E.g.C N

(beta electron emission )anti-neutrino

T 5730 yearstool for dating

archeo log ical objects

Carbon dating:The mechanism Carbon 14

concentrationconstant with time, at least over several times halflife of 5720 years, butalso calibratedwith tree ringdating and cavedeposits, good to 50,000 yearsago.

: 90% protons, 9% alpha part, …

4N7 + 1n0 → 14C6 + 1H1 + 0.62MeV

“Spallation”

The calibration curve

=Dep

artu

re fr

om m

oder

npr

e-in

dust

rial c

once

ntra

tion

in p

arts

per

100

0

Carbon dating: an accurate calibration curve

Nucleus has Excess energy

-

or +

Symbol

or +)

What happens to thisone then?

Enriched for nuclearweapon or fissionreactor use

Most of naturaluranium

Environmental hazard in the soil

(SEE SECTION 13.4)

Most probable,but manypossibilities(cf. Ex. 13.5);2.3 neutronsas average

Q = {M(235U) + m(n) – [M(94Sr) +M(140Xe) + 2m(n)]}c2

= [235.0439 - 93.9153 - 139.9216 – 1(1.0087)]uc2

= 0.1983uc2 = 0.1983 (931.5 MeV)= 184.7 MeV

Thermalneutron

Kin. Ener. 1 keVNegligible

2

Natural Uranium:U234 0.006%U235 0.72%U238 99.3%

Enriched Uranium:U234 >0.006%U235 5%U238 95%

“Yellowcake”(U3O8) UF6 gas

2 Brms aver

3k TV = (v ) = m

Uranium enrichment:

Iran in the news

Tank shell “penetrator”

1.7x denser than lead

Weapons-grade: Uranium- over 90% U-235; Plutonium over 93% Pu-239

2002 2006

http://www.isis-online.org/publications/iran/natanz03_02.html

New York Times

Energy Dept. Hesitates on Dealing With Uranium

By MATTHEW L. WALDPublished: April 1, 2008

WASHINGTON — The government is sitting on an inventory of partly processed uranium that could be sold for billions of dollars while prices are high, but the Energy Department is dawdling in deciding what to do with it, according to the Government Accountability Office.

The stockpile was formerly regarded as unwanted waste that would cost hundreds of millions of dollars to stabilize. But a steep increase in the price of uranium has made it valuable. “Recent dramatic gains in uranium prices present the U.S. government with an opportunity to gain some benefit from material that was once considered a liability,” said a report to Congress issued today.

“Unfortunately, DOE has not completed a comprehensive assessment of its options with sufficient speed to take advantage of current market conditions,” the auditors found. The Energy Department has said it would not sell too much of the uranium at once because that would hurt uranium producers. Processors and electric utilities, however, would benefit from lower prices for the raw material that ends up in nuclear power plants.

Uranium hexafluoride, the chemical form in which the material is stored, has gone from $21 a kilogram in November 2000 to $360 in the middle of last year, and $200 a kilo in February of this year.

The current value is about $7.6 billion, according to the auditors, but they said that it is not clear what direction prices will turn next. The stockpile could end up being worth as much as $20 billion or next to nothing. Experts say the current high prices are likely to stimulate the opening of new mines and new processing plants, increasing supplies and tending to drive prices back down. On the other hand, a resurgence in nuclear power, if it comes, would tend to push prices higher in the long run.

Breeder reactors--synthesizing their own fuel (see Section 13.5)

1.2 = the number of fissionable nuclei produced by each fission event

239Pu is a key fissile component in nuclear weapons, due to its ease of fissioning and availability.

*

*

(SEE SECTION 13.6)

Two approaches: U.S. - NIF – National Ignition Facility, Livermore. 192 laser beams compressing pellet of and to form a small “star”

European- Tokamak: Plasma trapped at high T in special B field

21H 3

1H

Radon in the earth: An environmental hazardU-238 (, t1/2 = 4 Billion yrs)multiple stepsRa-226(, t1/2 = 1600 yrs)

Rn-222(, t1/2 = 3.8 days)4 ppm of the earth’s crust

a = yeard = dayh = hoursmin = minutes

Radon in the earth: An environmental hazardThe largest single source of radiation exposure to the general public is naturally-occurring radon gas, which comprises approximately 55% of the annual background dose.

(picoCuries*/liter)

*1 Curie = 3.7 x 1010 nuclear decays per second

If shells incompletelyfilled, get net total spinand magnetic momenton nucleus:Nucleus Spin = S1H = prot ½2H = deuteron 113C ½14N 115N ½19F ½31P ½...

Nuclear Spins andMagnetic Resonance

~AUT0025

torqueB,

perpendicular to

tTORQUE

For the proton, with I = ½:For a nucleus with spin I = ½:

2 2

z I I

I I( I 1)

I m , m I , I 1,... I 1, I

IMAGING IN MEDICINEAND MEDICAL RESEARCH:

RF-- 20-60 MHzB 1.0-1.5 Tesla

NUCLEAR MAGNETIC RESONANCE IMAGING

x

x

x

x

Fourier transform spectroscopyMost applications of NMR involve full NMR spectra, that is, the intensity of the NMR signal as a function of frequency. Early attempts to acquire the NMR spectrum more efficiently than simple CW methods involved irradiating simultaneously with more than one frequency. It was soon realized, however, that a simpler solution was to use short pulses of radio-frequency (centered at the middle of the NMR spectrum). In simple terms, a short square pulse of a given "carrier" frequency "contains" a range of frequencies centered about the carrier frequency, with the range of excitation (bandwidth) being inversely proportional to the pulse duration (the Fourier transform (FT) of an approximate square wavecontains contributions from all the frequencies in the neighborhood of the principal frequency). The restricted range of the NMR frequencies made it relatively easy to use short (millisecond to microsecond) radiofrequency (RF) pulses to excite the entire NMR spectrum.Applying such a pulse to a set of nuclear spins simultaneously excites all the single-quantum NMR transitions. In terms of the net magnetization vector, this corresponds to tilting the magnetization vector away from its equilibrium position (aligned along the external magnetic field). The out-of-equilibrium magnetization vector precesses about the external magnetic field vector at the NMR frequency of the spins. This oscillating magnetization vector induces a current in a nearby pickup coil, creating an electrical signal oscillating at the NMR frequency. This signal is known as the free induction decay (FID) and contains the vector-sum of the NMR responses from all the excited spins. In order to obtain the frequency-domain NMR spectrum (NMR absorption intensity vs. NMR frequency) this time-domain signal (intensity vs. time) must be FTed. Fortunately the development of FT NMR coincided with the development of digital computers and Fast Fourier Transform algorithms.

Pickup coil

Pickup coil

Excitation coil

Excitation coil

IMAGING IN MEDICINEAND MEDICAL RESEARCH:

NUCLEAR MAGNETIC RESONANCE IMAGING

+ POSITRON EMISSION TOMOGRAPHY

PARTICLES AND ANTI-PARTICLES:MATTER AND ANTI-MATTER

3.17

Corrected

The positron:Postulated from theory(Pauli, Dirac)—late 1920’sObserved in expt.--1933

PARTICLES/ANTI-PARTICLESAPPLICATION IN MEDICINE/MEDICAL RESEARCH

If t2-t1 also measuredto e.g 10-10 s, the position along line further localized to (3.0x108)10-10 m = 3 cm—assists in image noise reduction

Nanoscience/Nanotechnology

The transistor

Experiment | TheoryDark Matter + Dark Energy | Supersymmetry? Strings?

Mediating ParticleForce

F

Fermions

JUNE, 2004:m = 178,0004,300 MeV/c2

2006:171 2 MeV/c2

(2 quarks)

(3 quarks)

Nanoscience/Nanotechnology

The transistor

Supersymmetry? Strings? + Dark Matter + Dark Energy

178 4 (’04)171 2 (‘06)

< 0.3 x 10-9 GeV/c2

(2006)

<1.9 x 10-4 GeV/c2

<0.018 GeV/c2

More recent nos.

Plus the Higgs boson:Lawrence Berkeley Lab Newsletter

Six outgoing “jets”

Force Mediating ParticleForce

F

+ Higgs boson—responsible for mass

The Particles-All Fermions

Best currentEst.- 115 - 180 GeV/c2

Nanoscience/Nanotechnology

The transistor

Experiment | TheoryDark Matter + Dark Energy | Supersymmetry? Strings?

Visible matter

Dark matterJ.A. Tyson, now UCD Physics

Approx. 20% of universe

See section 16.5 of Thornton and Rex

Dark matter

Dark EnergyInferred from an increase in the rate of expansion of the universe with time

E.g. supernovae at edge of visible universe (furthest back in time as seen by us)seem to be moving away more slowly

Einstein: The Cosmological Constant to keep the universe from closing,a blunder or profound insight, again?

The Makeup of the Universe

Matter- 5%

Dark Matter- 20%

Dark Energy- 75%

Nanoscience/Nanotechnology

The transistor

A lot of interesting physics (and

applications of it in technology,

medicine,…) to do at many levels!!

Experiment | TheoryDark Matter + Dark Energy | Supersymmetry? Strings?