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Transcript of Radioactivity - Institute for Structure and Nuclear ... Radioactivity Lecture 4 The Physics of...

  • Radioactivity

    Lecture 4 The Physics of radioactive Decay

    and Nuclear Reaction

  • Nature of Radiation

    • Deflection in electric field • α radiation is positively charged • β radiation is negatively charged • γ radiation is neutral • Stopping in material • α radiation has small range and

    large mass • β radiation has deep range and

    small mass • γ radiation has largest range and

    no mass – electromagnetic radiation

  • Origin of Radiation • Radioactive decay of unstable nucleus

    configuration (too many protons or too many neutrons) transitioning into a more stable form.

    • What represents a stable or unstable isotope configuration

    • Too many protons deflective Coulomb forces • Too many Neutrons reduce the strong binding

    force • Too many nucleons cannot be bound together

    by strong force • Too much deformation increases instability of

    nucleus. • Heavy deformed nuclei will spontaneously

    fission

  • Radiation as Energy Release A nucleus emits radiation of certain energy (E=hν for gammas and E=Ekin for particles) to reach the lowest possible energy configuration!

    2

    2 1 mvEkin =

    Energy release in gravitational potential

    Energy release in nuclear potential

    Particle decay to excited states with subsequent de-excitation by emission of gamma radiation

    β-decay

    γ-decay

    γ-spectrum

  • β- decay n ⇒ p+e-+ν

    β+ decay p ⇒ n+e++ν

    _

  • Alpha Decay of the Nucleus

    Occurs mainly for very heavy nuclei which are not stable against alpha emission

    Alpha particle α = 4He

    88 226

    86 222

    2 4Ra Rn He⇒ +

  • Nucleus conversion through α-decay

    Determine the end-product of the ‘yellow’ a-emitter: Z A

    N Z A

    NX X⇒ +− −

    −2 4

    2 α

    Z

    N

  • Beta Decay of the Nucleus

    β decay is the emission of an electron e- or positron e+ to convert a neutron to a proton or a proton to a neutron inside the nucleus 6 · e+  7 · e+ +1 · e-

    The β decay always converts along isobars

    Too many neutrons

    Too many protons

  • Gamma Decay of Nucleus

    excited states in nucleus

    Excitation of nucleus with subsequent characteristic γ emission

    Excited states correspond to vibration, rotation or quantum state excitation

    Ex

    γ emission l< 10-15 m

  • Nucleus conversion through β+,--decay

    Z A

    N Z A

    N

    Z A

    N Z A

    N

    X X X X

    ⇒ +

    ⇒ + − +

    +

    + − −

    1 1

    1 1

    β

    β Determine the end-product of the β+-emitter:

    Determine the end-product of the β--emitter:

    Z

    N

  • Energy in Nuclei According to Einstein’s formula, each nucleus with a certain mass m stores energy: E=mc2

    Proton mp = 1.007596 · 1.66·10-24 g = 1.672·10-24 g Neutron mn = 1.008486 · 1.66·10-24 g = 1.674·10-24 g Carbon m12C = 12.00000 · 1.66·10-24 g = 1.992·10-23 g Lead m208Pb = 207.797665 · 1.66·10-24 g = 3.449·10-22 g Uranium m238U = 238.050783 · 1.66·10-24 g = 3.952·10-22 g

    1 amu=1/12(m12C)=1.66 · 10-24 g Breaking up nuclei into their constituents requires energy

    www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53

    http://amdc.impcas.ac.cn/web/masseval.html

    http://amdc.impcas.ac.cn/evaluation/data2012/data/mass.mas12 http://www.nndc.bnl.gov/chart/reCenter.jsp?z=42&n=53 http://amdc.impcas.ac.cn/web/masseval.html

  • Some unavoidable unit considerations

    227

    23

    19

    2

    2

    /49.9311066.11 /300000

    10022.6 106022.11

    11

    cMeVkgamu skmc

    particlesgA JeV

    s mkgJ

    =⋅=

    = ⋅≡

    ⋅=

    ⋅ =

    http://en.wikipedia.org/wiki/Electronvolt

    http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt http://en.wikipedia.org/wiki/Electronvolt

  • Nuclear binding energy

    M · c2 < Z mp · c2 + N mn · c2

    The mass difference is the binding energy B

    The binding energy is the energy that needed to dissociate a nucleus into its single constituents. It is released when N neutrons and Z protons fusion together to form a nucleus with the mass number A!

    The mass M of the nucleus is smaller than the mass of its proton and neutron constituents!

    E=m·c2 N=3 neutrons

    Z=3 protons

  • Calculating the Nuclear Binding Energy

    B = (Z · mp+ N · mn- M) · c2 Binding energy B of nucleus ( ) ( ) ( ) ( )

    ( )

    ( ) nucleon

    J A

    CB

    J s mkg

    s mgsmg

    smggg

    cmmmCB Cnp

    12 12

    11 2

    11 2

    821625

    28232424

    212

    1017.1

    10404.110404.110404.1/1091056.1

    /10310992.110674.1610672.16

    66 12

    −−−−

    −−−

    ⋅=

    ⋅=  

      ⋅=

     

      ⋅=⋅⋅⋅=

    =⋅⋅⋅−⋅⋅+⋅⋅=

    ⋅−⋅+⋅=

    ( ) ( ) ( ) ( )

    ( )

    ( ) nucleon

    J A

    UB

    J s mkg

    s mgsmg

    smggg

    cmmmUB Unp

    12 238

    10 2

    10 2

    721624

    28222424

    2238

    10145.1

    10725.210725.210725.2/1091003.3

    /10310952.310674.114610672.192

    14692 238

    −−−−

    −−−

    ⋅=

    ⋅=  

      ⋅=

     

      ⋅=⋅⋅⋅=

    =⋅⋅⋅−⋅⋅+⋅⋅=

    ⋅−⋅+⋅=

  • Nuclear Potential and internal forces

    ( ) ( )

    MeVaMeVaMeVaMeVaMeVa oddNZAoddNZAaevenNZAa

    A ZAaAZZaAaAaB

    psymcsv

    pp

    symcsv

    34;23;72.0;8.16;5.15

    );(0);,();,(

    21

    3/43/4

    2 3/13/2

    =====

    +==⋅−=⋅+=

    + −

    ⋅−⋅−⋅⋅−⋅−⋅=

    −−

    δδδ

    δ

    http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 1 MeV = 1.602·10-13 J

    http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2 http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/liqdrop.html#c2

  • Nuclear Binding Energy Components

    Mass number

    1 MeV = 1.602·10-13 J

    Binding energy normalized to mass number B/A B /A

    (M eV

    /n uc

    le on

    )

  • Example: What is the binding energy of the oxygen isotope 18O?

    mp= 1.007596 · 1.66 · 10-24 g mn= 1.008486 · 1.66 · 10-24 g

    M(18O) = 17.99916 · 1.66 · 10-24 g

    Z=8, N=10, A=18

    Atomic Mass Unit: 1 amu=1/12(M12C)=1.66 · 10-24 g

    B = (Z · mp+ N · mn- M) · c2 B(18O) = 1.382 · 105 keV = 2.21·10-11 J B(18O)/A=1.23·10-12 J

    1g 18O contains 7.41·1011 J (W·s)

  • Nuclear Decay Processes

    A ⇒ B+b A(b)B

    14C(β-ν)14N 234U(α)230Th

    Decay energy is released in kinetic energy of emitted particles or in electromagnetic gamma radiation energy

    ( )

    JeVMeVQ

    MeVMeVMeVMeVQ

    BBBQBBBQ cmcmmQ

    U

    U

    ThHeUUAbBd

    AbBd

    127

    22

    104.81025.55.52

    5.52128.12755296.28325.1779

    234

    234

    2304234234

    −⋅=⋅==

    =−+=

    −+=−+= ⋅−⋅+= JeV 19106.11 −⋅=

  • Nuclear Reactions and Energy Release

    a

    A

    Frederic Joliot and Irene Curie at Paris had observed the first nuclear reaction. Enrico Fermi showed the existence of neutron induced reactions, which produce artificial radioactivity.

    Nuclear reactions can produce energy Q > 0 exothermic or need energy Q < 0 endothermic

    A(a,b)B Q = (mA+ ma- mB- mb)·c2

    Q = BB+ Bb- BA-BB

    Nobel Prize 1938

    Difference of masses in entrance and exit channel determines Q

  • Q value of nuclear reaction process

    a

    A

    b

    B

    A+a ⇒ B+b

    A(a,b)B

    projectile

    target

    product

    recoil ( ) ( ) ( ) ( )

    reactioncendothermi0 reactionexothermic0

    22

    < >

    +−+= ⋅+−⋅+=

    Q Q

    BBBBQ cmmcmmQ

    aAbB

    aAbB

  • Example: Nuclear Reaction energy budget

    isotope B (J)

    2H 3.34131·10-13

    4He 4.53297·10-12 12C 1.47643·10-11

    119Pd 1.59643·10-10

    238U 2.88631·10-10

    ( )

    JJJQ UBPdBPdBQ

    QPdU

    JJJQ HBHB