9/5/2015 intro; em radiation; radioactivity p. 1 of 63 illinois institute of technology physics 561...

04/19/23 Intro; EM Radiation; Radioactivity p. 1 of 63

Illinois Institute of Technology

PHYSICS 561

RADIATION BIOPHYSICSCourse Introduction:

Electromagnetic Radiation;Radioactivity I

ANDREW HOWARD3 June 2014


Radiation Biophysics: Introduction

What we’re trying to do:provide you with an understanding of what happens when ionizing radiation interacts with biological tissue.

Most of you are in the Health Physics curriculum:there, you’re learning about ionizing radiation– how it is produced– what it is used for– how to deliver it– how to quantify it– how to minimize exposure of people and things to it.


Introduction (continued)

You have also learned about the biological effects of radiation in other courses.

In this course the emphasis is on the biological effects, both harmful and beneficial, of radiation.

But to put those biological issues in context:– We’ll discuss radiation physics and radiation chemistry.– We won’t spend a lot of time on those subjects:

you’ve dealt with those subjects in other courses.


Who is your instructor?

I am primarily in the biology faculty within the Biological and Chemical Sciences Department at IIT.

But my secondary appointment is in the physics department, and my graduate degree is in physics, so I'm reasonably familiar with physics and chemistry as well as biology.

http://www.iit.edu/~bcps/

http://www.iit.edu/~bcps/

http://www.iit.edu/


Am I qualified to teach this?

I’m a crystallographer:– I use X-ray diffraction to study the 3-D

structures of large biomolecules– I am not a health physicist by specialization– My research is often affected by concerns for

the radiation safety of my experiments.– I'm a consumer of rad. biophysics knowledge.

I postdoc’d in toxicology in a DOE lab:mechanistic studies stuck with me


Why I may be a bit incoherent a few times this summer

http://www.renfair.com/bristol/


How will this course work?

Live meetings: Tuesday and Thursday, 10 am- 12:50pm at IIT from 3 June through 24 July (plus an external final), in Stuart Building Room 213

Internet: 6-18 hours behind. Internet students are welcome to visit the live

section, which currently has no enrollees Primarily lectures, but with discussion Internet students: Communicate with one another

and with me via the discussion board and e-mail– It’s the only way I’m going to get to know you.– Be brazen! Be daring!

Special schedule, early July

I will be attending a wedding in Oxford UK over Independence Day weekend

Rescheduled classes:– Class on Tuesday 1 July Monday 30 June– Class on Thursday 3 July Tuesday 1 July– Class on Tuesday 8 July Thursday 10 July– Class on Thursday 8 July Friday 11 July



Homework

We will start every class except this one by going over the homework assignment.

The homework is generally due at 11:59 p.m. on the Friday or Monday, 3-5 days after class, so we won't answer the homework questions in class, but we will discuss how the problems work, and if there are items that require clarification we'll provide them then.

It’s okay to turn assignments in late.


Course Plans (continued)

2 midterms and a final– Midterms 19-20 June, 2-4 July

– Final 24-26 July

– All exams are closed-book, closed-notes, apart from a help-sheet that I will provide.

– You may use a calculator, but not a programmable

– All exams will be conducted outside of class sessions: we need all the class time for content

Detailed schedule is on the course Blackboard site


Course Sources Edward L. Alpen, Radiation Biophysics,

– 2nd Ed.: San Diego: Academic Press, 1998.520 pp..., cloth. ISBN-10 0120530856.

– We’ll work closely from textbook except in our discussion of radiation chemistry (chapter 6) and two lectures at the end of the course on biochemistry, hormesis, and some other supplementary topics

– The textbook is not a required purchase;I’ll cover most of what is in the book

Supplemental readings:HTML, books, journal articles


Using Blackboard

Portal to online lectures Posting site for HTML and PowerPoint lecture

materials Exam keys will be emailed to you Posting site for peer-reviewed literature Discussion board: Use it!

– Your opportunity to mull over the material– Chance to get to know your classmates– Content-related participation does get graded


Inconsistencies

It’s possible that you’ll see an inconsistency between the assignments as posted on the Assignments section on Blackboard and the overall Assignments webpage. Which is authoritative?

Answer: the Assignments section on Blackboard … And while we’re on the subject:

Submit your answers to the Blackboard Assignments page too!


History of radiation biophysics I

Early characterizers of the properties of X-rays and radioactivity:– Wilhelm Röntgen: X-rays, 1895– Becquerel: radioactivity– Rutherford: radioactive chain

decay– The Curies: radium, polonium


History II Edison’s fluoroscope: 1896

Don’t talk to me about X-rays,I am afraid of them. -T.A.E., 1903

However: it was his employees, not Edison, who got sick!


Radiation and Medicine: 1895

First medically observable deleterious effect from X-rays was recorded less than six months after Roentgen's discovery of X-rays. So the history of radiation biophysics goes back almost as far as the history of X-rays


Quantities, Units, and Definitions

The world of radiation research has gone through a major change in the units that it uses to express quantities. As recently as the 1970's when I was learning radiation quantitation, the traditional units for activity, dose, energy imparted, and equivalent dose were still in common use. In this course we will use the more modern units except in dealing with older research papers.


Quantities, Units, DefinitionsQuantity Exposure

(em only)Dose Energy

Imparted

Definition Q/m Ed/m Ed

SI Unit C kg-1 Gray Joule

Unit definition

J kg-1 kg m2s-2

Old Unit Röntgen Rad Erg

Definition 1 esu cm-3 100 erg g-1 g cm2s-2

Conversion 1 R = 2.58 * 10-4 C kg-1

1 Gy = 100 Rad

1 J = 107 erg


Additional Quantities:Equivalent Dose

Effects of a dose depend on how much energy is deposited per unit mass and on how influential that energy is in the medium:

HT,R = DRWT,R

(DR=dose, WT,R= weight factor)for tissue T, radiation type R.

If R is 60Co photons, WR=1 (reference type) Unit: Sievert (1 J/kg)


Honorees

Louis H. Gray (1905-65)

Rolf M. Sievert(1896-1966)


RBE and Kerma

RBE (relative biological effectiveness):– describes weight factors for

specific biological endpoints (e.g. carcinogenesis) as well as specific radiation types.

– Often used in context of radiation-induced tumors and other long-term problems.

Kerma: Kinetic Energy Released to the Medium– Let EK =initial kinetic

energy of all charged particles liberated. Then Kerma K = EK / m

– Dimensions of dose(book says energy—that’s wrong)

– Units: Gy or rad.


Fluences and Flux Densities

Let N = # particles entering a sphere with cross sectional area a (total area a = 4r2)

Particles enter during time interval t—Then—

Particle fluence = = N / a Particle flux density = = / t


Fluence and Flux Visuals

Area through which particles enter = a

Total Surface area a = 4r2

N particles enter in time t Particle fluence = N/a Flux Density = = /t

a

N


Energy Fluence, Flux Density

Let Ef = sum of energy (exclusive of rest energy) of all particles entering sphere of cross-sectional area a

Energy fluence: Ef /a Energy flux density: /t


Linear Energy Transfer (LET)

LET defined as dEL/dl, where dEL is the energy locally imparted to the medium over the length interval dl.

Dimensions: Energy / length; units: J/m restricted range stopping power: don’t look

for energy deposited far from path.


What does LET depend on?

Nature of radiation– Alpha particles can be stopped by paper– Betas can be stopped by aluminum– Photons can get through almost anything

Nature of medium (density, chemistry) Energy of radiation


LET’s dependence on energy

Dependence on energy manifests itself often in subtle ways:e.g. more absorption near absorption edges.


Charged Particle Equilibrium

CPE exists at a point p centered in a volume V if each charged particle carrying a certain energy out of V is replaced by another identical charged particle carrying the same energy into V. If CPE exists, then dose = kerma.


Radioactivity Measurements Let dP be the probability that a specific

nucleus will undergo decay during time dt. Decay constant of a nuclide in a particular

energy state is = dP/dt. Half-time or half-life: time required for half

of starting particles to undergone transitions. T1/2= (ln 2) / (not ln (2/ ), as the book claims)


Activity Let dN = expectation value (most likely number) of

nuclear transitions in time dt. Then activity A = dN/dt = -N

(note that the minus sign is just keeping track of disappearance rather than appearance)

If you don’t understand that, you will fail the Health Physics Comprehensive Exam!

Dimensions: time-1

Units: 1 becquerel = 1 disintegration /sec Old unit: Curie: 3.7•1010 s-1


Electromagnetic Radiation

Much of this course deals with the interaction between electromagnetic radiation (usually ionizing) and matter

So we need to review the properties of electromagnetic radiation

EM radiation encompasses a wide rangeof energy / wavelength / frequency– Ionizing radiation:

E = 1KeV - up, = 0.81 nm -down– Visible light is lower-energy (E~1eV, ~500 nm)


The Electromagnetic Spectrum


… or in graphical form


Laws of Electromagnetism

The four major rulesof electrodynamics:– Coulomb’s law

(F = kq1q2r-2)– Biot-Savart law

(dB = (µ0/4)dlxr/r3)– Faraday’s law

(E = -B/t)– Conservation of charge

Charles-Augustin de Coulomb

Jean-Baptiste Biot

Félix Savart

Michael Faraday


Maxwell’s contribution

These rules predated Maxwell. He showed they could be made self-consistent by recognizing that a changing electric field induces a magnetic field; thus the integral and differential forms of Maxwell’s equations.

James Clerk Maxwell


What Maxwell’s laws mean for radiation

The electromagnetic field travels away from its source with velocity = 3 * 108 m /sec.

This turns out to be the velocity of light, so evidently light is an electromagnetic wave!

Relationship between frequency and wavelength:c =


Planck’s contribution

Planck sought to understand radiation in a cavity by assuming that the atoms in the cavity were electromagnetic oscillators with characteristic frequencies and the oscillators would absorb and emit radiation

He also posited that the oscillators were constrained to have energiesE = (n+½)hwhere = frequency, h = a constant


Einstein’s photoelectric effect Energy of photons goes into

enabling the electrons to escape from the surface, plus their kinetic energy after they do so:Ephoton = h = E0 + Kmax

Here E0 is the work function,Kmax is max electron energy


Special Relativity

Einstein modified Galilean relativity, under which velocities are additive.

Galileo: automobile velocity with respect to ground = u = v + w

Einstein says: u < c so we need new rules!


Special Relativity: Energy

Einstein’s new rules require thattime & distance formulae depend on velocity

Corrections are significant in nuclear reactions, radiation scattering, and accelerators, so we study them here a little

They also give rise to the concept of relativistic energy

Hendrick Lorentz


Rest energy and mass

If v = 0, E = E0 = m0c2; this is rest energyif m0 is the rest mass, i.e. the mass as it is ordinarily defined.

We can summarize the results by defining a relativistic mass m so that we can say E = mc2 = m0c2 where m = m0

For v = 0.1c, m = 1.05m0;for v = 0.98c, m = 5m0.


Atomic Structure

JJ Thomson (1897): heavy nucleus with electrons surrounding it.

Rutherford showed that the nucleus had to be very small relative to the atomic size


The Bohr Model

Bohr model: quantized angular momentum so that radiation is emitted in quanta equal to difference between energy levels of the atom. Used classical energy calculations!


Bohr model: radius

Quantized angular momentum mvr = nh/2But this is associated with coulombic attraction for which the centripetal force must equal the coulombic force:

F = mv2/r = kZe2/r2, so r = kZe2/mv2

Thus v = nh/(2mr) = 2kZe2/nhso r = n2h2/(42kZe2m)

For n=Z=1,r = h2/(42ke2m) = 0.529*10-10 m = Bohr radius


Bohr model: Electron Energies

Velocity = v = 2kZe2/(nh) Kinetic energy = 1/2mv2 = 22k2Z2e4m/(n2h2) Potential energy = -kZe2/r = -42k2Z2e4m/(n2h2) Total energy = KE + PE = -22k2Z2e4m/(n2h2) Photons emerge from transitions from one value of n

to another. Transition from n = 3 to n = 2 gives

photon energy = -22k2Z2e4m / [(1/9 - 1/4) h2]= 1.89 eV


DeBroglie Wave Theory

So: we’ve allowed electromagnetic radiation to behave as a wave and a particle. We can express momentum of light as

P = E/c = h/c = h/ Can we also talk about matter behaving both as a

wave and a particle? Yes. Particles can exhibit interference effects associated

with wave behavior. Wavelength = h/P = h / (mv)


Wave Behavior in electrons

Nonrelativistic approximation:KE = (1/2)mv2 so = h/(mv) = h(2(KE)m)-1/2

Further, since the angular momentum mvr is quantized (mvr = nh/(2)), we can say

2r = n So we can say that the circumference of the

electron’s orbit is an integer multiple of the electron’s wavelength! Standing waves!


Assignment associated with this lecture:

Alpen, chapter 2, problem 1:Assume an oscillating spring that has a spring constant, k, of 20 Nm-1, a mass of 1 kg, and an amplitude of 1 cm. If Planck’s radiation formula describes the behavior of this system, what is the quantum number, n. What is E if n changes by 1? Recall from freshman physics that the frequency of a simple oscillator is given by = (1/2)(k/m)1/2


Assignment, continued:

Alpen, ch.2, problem 4:A proposed surface for a photoelectric light detector has a work function of 2.0*10-19 J. What is the minimum frequency of radiation that it will detect? What will be the maximum kinetic energy of electrons ejected from the surface when it is irradiated with light at 3550Å (355 nm)?



Alpen, chapter 2, problem 5:In the previous problem, what is the de Broglie wavelength of the maximum kinetic energy electron emitted from the surface? What is its momentum?



(from my head…):The Advanced Photon Source (APS) at Argonne National Laboratory produces X-rays from electrons that have been accelerated to an energy of approximately 7 gigaelectron volts. This corresponds to an electron velocity very close to the speed of light. If the APS electron’s velocity is v, calculate c-v in ms-1 to 2 significant figures.

Assignment, concluded:

5. Assume the electron described above is traveling at constant speed around a circular path with circumference 1.1 km. Compute the acceleration a of the electron in m s-2 and as a multiple of the gravitational acceleration g.


A suggestion

Note that there are hints on how to answer these questions within the old posts to the course Discussion Board. I encourage you to look for those. If you read a few other posts along the way, everyone benefits!



Some nuclei decay Radioactivity is the process by which

unstable nuclei change state in order to arrive at a lower-energy configuration

We need to familiarize ourselves with the processes by which this occurs and how it gives rise to ionizing radiation

We care about this in physics 561 because radioactivity is both a hazard and a diagnostic and therapeutic tool


Radioactivity

Nuclear Stability Mass Decrement Alpha Emission Negative Beta Emission Positive Beta Emission Electron Capture Spontaneous Fission


Four forces

By ~1950: clear that all known physical interactions could be characterized by 4 forces:

Force Strength Range Exchanged particles

Quantum theory

Gravity Weak Infinite Graviton Poor

Electro-magnetism

Moderate Infinite Photon QED

Weak nuclear

Moderate Limited W+,W-,Z Electro-weak

Strong nuclear

Strong Limited Gluons QCD


Radioactivity Nucleus is subject to all four of these forces,

although gravity will be ignored here. Strong nuclear force overcomes Coulombic

repulsion and enables nucleus to assemble. Weak nuclear force is responsible for differences

between protons and neutrons and thereby explains beta decays.

Stable nuclei are those for which the combination of interactions produces a nucleus that is already in a low-energy configuration and therefore won’t decay.


Stable and Unstable Elements Every element has ≥1 unstable isotope, i.e. one that

undergoes radioactive decay Most elements with Z < 92 have at least one stable isotope We’ll examine radioactivity in terms of the transitions under

which a nucleus decays Radioactivity has various influences on biological tissue:

– Ionization of biological macromolecules

– Indirect effects, often via free radicals

– Medical applications: therapy, diagnostics, . . .

Region of stability and nuclear decay

decays: up & left. np+e-+’ decays: down & right: pn+e++ 2+: 2 units down & left: A

ZQ A-4Z-2R

: no effect here: Q* Q


Z

N

Z=N line

α β+

β-


Rules Stable nuclei of even Z more numerous than odd Z. Stable nuclei of even N more numerous than odd N. Stable nuclei of even A more numerous than odd A. In general, stable nuclei of even A have even Z. Some

exceptions exist, such as 2H, 6Li, 10B, and 14N Only two stable structures are known for which Z is greater than

N: 3He and 1H Examining what happens to the N/Z ratio in a typical alpha

decay:226Ra 222Rn + + + QZ = 88 86 (number of protons)N = 138 136 (number of neutrons)N/Z = 1.5682 1.5814


Mass Energy of - Particle

Ignoring binding energy, 2 protons + 2 neutrons:

2moc2(neutron) 1978 MeV

2moc2(proton) 1976 MeV--------------

Mass Energy = 3954 MeV

Kinetic Energy ~ 4 MeV

But, in fact, ignoring binding energy is a bad idea, because it does affect the real mass energy, which is about 28.27 MeV (0.7%) lower than that. We’ll come back to that idea later in the lecture.


Beta DecaysNegative Electron Decay

Positive Electron Decay

Spontaneous annihilation


Energy - Wavelength Relationship for Photons• The general relation connecting wavelength

to energy is E = hc /

• Specifically, for energy in eV and wavelength in Å: E = 12398.4 /

• For energy in MeV and wavelength in Å:E = 0.0123984 /

• for either of the photons emitted in a positron-electron annihilation:E = 0.511 MeV so = 0.0123984 / 0.511= 0.02426 Å = 2.426 pm.


Charting Decay Schemes

We can sometimes find multiple pathways, each with multiple steps, as with 74As here(this is fig. 3.4, p. 37, in Alpen)

9/5/2015 intro; em radiation; radioactivity p. 1 of 63 illinois institute of technology physics 561...

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