and decays, Radiation Therapies and Diagnostic, Fusion and Fission This Lecture: Radioactivity, Nuclear decay Radiation damage, radiation therapies.

β and γ decays, Radiation Therapies and Diagnostic,

Fusion and Fission

This Lecture: Radioactivity, Nuclear decay Radiation damage, radiation therapies and diagnostic

Evaluations for Prof. T. Montaruli today

Previous lecture: nuclear physics

Final Exam

• Fri, Dec 21, at 7:45-9:45 am in Ch 2103 • About 40% on new material• 2 sheets allowed (HAND WRITTEN!)

• The rest on previous materials covered by MTE1 MTE2 MTE3.

New material not covered by MTE1,2,3

• Ch 40.4-5 particle in a box: wave functions, energy levels, photon absorption and emission, 40.10 tunneling

• Ch 41.1-3 H-atom quantum numbers and their meaning, wave functions and probabilities, electron spin

• Ch 41.4-6 Pauli exclusion principle, multi-electron atoms, periodic table, emission and absorption spectra

• Ch 41.8 Stimulated emission and Lasers

• Ch 42.1-3 Nuclear structure, atomic mass, isotopes, binding energy, the strong force

• Ch 42.5 Radioactivity, Ch 42.6 Nuclear decay, Ch 42.7 Biological applications

Women Nobel PrizesThe only 2 female Nobel Prizes in Nuclear

Physics!

Maria Goeppert-Mayer 1963 Shell Model of Nucleus

1903 Marie Curie (with Pierre)in recognition of the extraordinary services they have rendered by their joint researches on the radiation phenomena discovered by Professor Henri Becquerel

5

Nuclear Physics• Strong force: attractive force keeping p and n in nucleus (short

range) • It is convenient to use atomic mass units to express masses

– 1 u = 1.660 539 x 10-27 kg– mass of one atom of 12C = 12 u

• Mass can also be expressed in MeV/c2

– From rest energy of a particle ER = mc2

– 1 u = 931.494 MeV/c2

• Binding energy: mnucleus < Zmp + (A-Z)mn = Zmp + Nmn

• The energy you would need to supply to disassemble the nucleus into nucleons Ebinding = (Zmp+Nmn-mnucleus)c2 = (Zmp+Zme+Nmn+ -Zme-mnucleus)c2 =(ZmH + Nmn - matom) c2

5

C12

6

6

Fission and Fusion

Stable and Unstable Isotopes

Isotope = same ZIsotone = same NIsobar = same A

Stability of nuclei• Dots: naturally occurring isotopes.

• Blue shaded region: isotopes created in the laboratory.

• Light nuclei are most stable if N=Z

• Heavy nuclei are most stable if N>Z

• As # of p increases more neutrons are needed to keep nucleus stable

• No nuclei are stable for Z>83

Radioactivity

• Discovered by Becquerel in 1896 • spontaneous emission of radiation as result of

decay or disintegration of unstable nuclei• Unstable nuclei can decay by emitting some

form of energy

• Three different types of decay observed:Alpha decay ⇒ emission of 4He nuclei (2p+2n)Beta decay⇒ electrons and its anti-particle (positron)Gamma decay⇒ high energy photons

Penetrating power of radiation

• Alpha radiation barely penetrate a piece of paper (but dangerous!)

• Beta radiation can penetrate a few mm of Al• Gamma radiation can penetrate several cm of

lead

Is the radiation charged?

• Alpha radiation positively charged• Beta radiation negatively charged• Gamma radiation uncharged

The Decay Rate• probability that a nucleus decays during Δt

• number of decays (decrease)= NxProb=rNΔt N=number of independent nuclei

Constant of proportionality = decay rate (in s-1)

The number of decays per second is the activity

# radioactive nuclei at time t

# rad. nuclei at t=0

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Prob(in Δt) = rΔt

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ΔNΔt

= −rN

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N(t) = N0e−rt

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R =ΔN

Δt= rN

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τ =1

rtime constant

The half-life

• After some amount of time, half the radioactive nuclei will have decayed, and activity decreases by a factor of two.

• This time is the half-life

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N(t1/ 2) =N0

2= N0e

−rt1/2

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t1/ 2=ln2

r= τ ln2 = 0.693τ

Units

• The unit of activity, R, is the curie (Ci)–

• The SI unit of activity is the becquerel (Bq)–

• Therefore, 1 Ci = 3.7 x 1010 Bq

• The most commonly used units of activity are the millicurie and the microcurie

An Example• 232Th has a half-life

of 14 x109 yr

• Sample initially contains: N0 = 106 232Th atoms

• Every 14 billion years, the number of 232Th nuclei goes down by a factor of two.

N0

N0/2N0/4

N0/8

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N(t1/ 2) =N0

2= N0e

−rt1/2

Radiocarbon dating

• 14C (Z=6) has a half-life of 5,730 years, continually decaying back into 14N (Z=7).

• In atmosphere very small amount! 1 nucleus of 14C each 1012 nuclei of 12C

If material alive, atmospheric carbon mix ingested (as CO2), ratio stays constant.

After death, no exchange with atmosphere. Ratio changes as 14C decays

So can determine time since the plant or animal died (stopped exchanging 14C with the atmosphere) if not older than 60000 yr

Carbon dating

A fossil bone is found to contain 1/8 as much 14C as the bone of a living animal. Using T1/2=5,730 yrs, what is the approximate age of the fossil?

A. 7,640 yrs

B. 17,190 yrs

C. 22,900 yrs

D. 45,840 yrs

Factor of 8 reduction in 14C corresponds to three half-lives.

So age is 5,730 x 3 =17,190 yrs

Heavy nucleus spontaneously emits alpha particle

Decay processes: α = 4He

• nucleus loses 2 neutrons and 2 protons.

• It becomes a different element (Z is changed)

• Example:

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92238U→ 2

4He+ 90234Th

92 protons146 neutrons

90 protons144 neutrons

2 protons2 neutrons

Alpha particle

A quantum process• This is a quantum-mechanical process

– It has some probability for occurring.• For every second of time, there is a probability

that the nucleus will decay by emitting an α-particle.

• This probability depends on the width of the barrier

• The α -particle quantum-mechanically tunnels out of the nucleus even if

energy is not > energy barrier

Potential energy of α in the daughter nucleus vs distance

Coulomb repulsion dominates

Nuclear attraction dominates

Disintegration Energy• In decays energy-momentum must be conserved • The disintegration energy appears in the form of kinetic energy

of products

MXc2 = MYc2 + KY + Mαc2 + Kα ⇒ ΔE=KY Kα = (Mx – My – Mα)c2

Textbook: neglect KY since

Mα<<MY⇒ ΔE=Kα ~ (Mx – My – Mα)c2

• It is sometimes referred to as the Q value of the nuclear decay

Decay sequence of 238U

Number of neutrons

Num

ber

of

pro

ton

s

α decay

Radon• Radon is in the 238U decay

series

• Radon is an α emitter that presents an environmental hazard

• Inhalation of radon and its daughters can ionize lung cells increasing risk of lung cancer

• Madison is in Zone 1!

• In USA 20000 people die but a Geiger can help to identify problem in houses

• Also used to predict Earthquakes!

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 1 Highest Potential (greater than 4 pCi/L)

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.Zone 2 Moderate Potential (from 2 to 4 pCi/L)

http://www.radonwisconsin.com/

http://www.radonwisconsin.com/

Activity of Radon• 222Rn has a half-life of 3.83 days.• Suppose your basement has 4.0 x 108

such nuclei in the air. What is the activity?

We are trying to find number of decays/sec.

So we have to know decay constant to get R=N

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r =0.693

t1/ 2

=0.693

3.83days× 86,400s /day= 2.09 ×10−6 s

R =dN

dt= rN = 2.09 ×10−6 s× 4.0 ×108nuclei = 836decays /s

R = 836 decays /s×1Ci

2.7 ×1010decays /s= 0.023μCi

Radiation damageThe degree and type of damage caused by radiation depend on• Type and energy of the radiation• Properties of the absorbing matter

Radiation damage in biological organisms is primarily due to

ionization effects in cells that disrupts their normal functioning

Alpha particles cause extensive damage, but penetrate only to a shallow depth

Gamma rays can cause severe damage, but often pass through the material without interaction

Other kind of radiations: eg. neutrons penetrate deeper and cause more damage.



Radiation Poisoning Killed Ex-Russian Spy

The British authorities said today that A. V. Litvinenko, a former Russian Federal Security

Service liutenant-colonel, and later dissident, died of radiation poisoning due to a rare and highly radioactive isotope known as Polonium 210.

Highly radioactive metalloid discovered by M. Curie

A N Isotopic T1/2 Activity mass (u) (d) (uCi)

210Po 84 126 209.98 140 0.1

Produced by bombarding bismuth-209 with neutrons in nuclear reactors. In the decay 210P creates 140 W/g so 1/2 a gram reaches 500 °C. Considered to power spacecrafts.Used in many daily applications: eg anti-static brushes in photographic shopsDangerous only if ingested because it is an α emitter.



Radiation Levelsrad (radiation absorbed dose) = amount of radiation that increases the energy of 1 kg of absorbing material by 1 x 10-2 J

RBE (relative biological effectiveness = # of rads of X or gamma radiation that produces the same biological damage as 1 rad of the radiation being used

rem (radiation equivalent in man) =

dose in rem = dose in rad x RBE

Upper limit suggested by US gov0.50 rem/yr



Ground 0.30 rem/yr

Mercury 9 60.6 rem/yr

Apollo 14 146.2 rem/yr

MIR Station 34.9 rem/yr

Space Station 36.5 rem/yr

Beta decay• Nucleus emits an electron or a positron• Must be balanced by a positive or negative

charge appearing in the nucleus.

This occurs as a n changing into a p or a p into a n

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ZAX→Z +1

AY + e−

ZAX→Z−1

AY '+e+

Example of β-decay• 14C (radioactive form of carbon) decays by β-

decay (electron emission).• Carbon Z = 6, 14C has (14-6)=8 neutrons.• A new element with Z = 7

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614C→ 7

14 N+e−

Beta decay decreases number of neutrons in nucleus by

oneincreases number of protons in nucleus by one

We do not see it, but to explain this decay an anti-neutrino is needed

The Positron and Antimatter• Every particle now known to have an antiparticle.

• Our Universe seems to contain more matter (we are lucky otherwise everything would annihilate into photons!)



Positron 1st detection in cosmic rays through bending in a B-field and a bubble chamber (Anderson 1932)

Decay Quick Question

20Na decays in to 20Ne, a particle is emitted? What particle is it?

Na atomic number Z = 11Ne Z = 10

• Alpha• Electron beta• Positron beta• Gamma

20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to a neutron (0 charge) in this decay. A positive particle had to be emitted.

20Na has 11 protons, 9 neutrons20Ne has 10 protons, 10 neutronsSo one a proton (+ charge ) changed to a neutron (0 charge) in this decay. A positive particle had to be emitted.

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p → n + e+ + ν e

Nuclear Medicine: diagnostic• Basic Idea:

– Inject patient with radioactive isotope (tracer) that decays in a positron

– Positrons annihilate with electrons into gamma rays– Reconstruct the 3-D image

Positron Emission Tomography image showing a tumor

Positron Emission Tomography - PET

Basic Idea:– A short-lived radioactive

tracer isotope emits a positron

– Positron collides with a nearby electron and annihilates

– e+ + e- → 2γ• Two 511 keV gamma rays are

produced

• They fly in opposite directions (to conserve momentum)

Nucleus(protons+neutrons)

electrons

Isotope Max. Positron Range (mm)

18F 2.6

11C 3.8

68Ga 9.0

82Rb 16.5

Gamma Photon #1

Gamma Photon #2

e+-e-→γγ

Emission Detection

• If detectors receive gamma rays at the approx. same time, we have a detection

• Nuclear physics sensor and electronics

Ring of detectors

• Each coincidence event represents a line in space connecting the two detectors along which the positron emission occurred.

• Coincidence events can be grouped into projections images, called sinograms.

• Sinograms are combined to form 3D images

Image Reconstruction

Cancer Radiation Therapy• 50-60% of cancer patients treated with radiation

• Radiation destroys the cancer cells' ability to reproduce and the body naturally gets rid of these cells.

• Although radiation damages both cancer cells and normal cells, most normal cells can recover from the effects of radiation and function properly.

• Ionization (stripping atomic electrons) makes nuclear radiation dangerous

Used radiations:

• X and γ-rays (60Co) from 20 KV to 25 MV

• Pion Therapy under study, less

invasive then photons

• Neutrons,protons,..QuickTime™ and a

TIFF (Uncompressed) decompressorare needed to see this picture.

Gamma decay

• Both α and β-decays can leave the nucleus in excited state

• The nucleus can decay to a lower energy state (eg the ground state) by emitting a high energy photon (1 MeV-1 GeV)

The X* indicates a nucleus in an excited state

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92238U→ 90

234Th +α

Decay Question?

Which of the following decays is NOT allowed?

1

2

3

238 = 234 + 4

92 = 90 + 2

214 = 210 + 4

84 = 82 + 2

14 = 14+0

6 < 7+0

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84214Po→ 82

210Pb+24He

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614C→ 7

14N + γ

and decays, Radiation Therapies and Diagnostic, Fusion and Fission This Lecture: Radioactivity, Nuclear decay Radiation damage, radiation therapies.

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