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  • ! and " 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


    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

    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




    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


    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 !t

    number of decays (decrease)= NxProb=rN!t N=number of independent nuclei

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

    The number of decays per second is the activity

    # radioactive nuclei at time t

    # rad. nuclei at t=0


    Prob(in "t) = r"t



    "t= #rN


    N(t) = N0e"rt


    R ="N

    "t= rN


    " =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

    ! !

    N(t1/ 2) =


    2= N



    t1/ 2


    r= " ln2 = 0.693"


    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 = 10

    6 232Th atoms

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






    N(t1/ 2) =


    2= N


    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: $ = 4He

    nucleus loses 2 neutrons and 2 protons.

    It becomes a different element (Z is changed)






    4He +



    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 $-particle.

    This probability depends on the width of the barrier

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

    energy is not > energy barrier

    Potential energy of $

    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 = MYc

    2 + KY + M$c2 + K$ # %E=KY + K$ = (Mx My M$)c


    Textbook: neglect KY since


  • 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 $ 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 gov

    0.50 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




    Z +1

    AY + e





    AY '+e


    Example of !-decay

    14C (radioactive form of carbon) decays by !-

    decay (electron emission).

    Carbon Z = 6, 14C has (14-6)=8 neutrons.

    A new element with Z = 7





    14N+ e


    Beta decay decreases number of neutrons in nucleus by one increases 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 = 11

    Ne Z = 10

    A. Alpha

    B. Electron beta

    C. Positron beta

    D. 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.


    p" n + e+

    + # 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:


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