the abc’s of r adioactivity physics of atomic nuclei - lecture 3 peggy norris,...
TRANSCRIPT
WHAT IS RADIATION?
Radiation is energy released after being stored in atoms Radiation can be natural or man-made Radiation can be in the form of particles or
electromagnetic radiation When radiation comes from the nucleus of an atom it is
called radioactivity
We will be focusing on ionizing radiation and its health effects.
ATOMS
… are made of
Electrons and the Nucleus
Electrons
… are very light but take up most of the space in an atom
The nucleus
… lies at the center of the atom, has almost all of the mass but takes up almost none of the space inside an atom
THE NUCLEUS
The number of protons in a nucleus is equal to and determines the number of orbiting electrons• determines the chemistry• determines the element name
An atom is electrically neutral (# of protons (q=+1) = number of electrons (q=-1))
An ion is a charged atom; can be positive (electron removed) or negative (electron added)
ISOTOPES
•Uranium-238 (238
92U)
92 protons, 146 neutrons, mass 238
•Uranium-235 (235
92U)
92 protons, 143 neutrons, mass 235
•Hydrogen (11H)
1 proton, 0 neutrons, mass 1
•Deuterium (21D)
1 proton, 1 neutron, mass 2
•Tritium (31T)
1 proton, 2 neutrons, mass 3
•Helium (42He) (a-
particle)
2 protons, 2 neutrons, mass 4
•Helium-3 (32He)
2 protons, 1 neutron, mass 3
THE NUCLEAR LANDSCAPE
Where do they come from?
Natural Radioactivity … natural processes occurring in the sun or other stars, in our atmosphere, and part of the gas clouds that formed our solar system.
Man Made Radioactivity … Reactors, accelerators etc.
• Most elements have several stable isotopes. Every element has many unstable (radioactive) isotopes. • There are about 200 different stable isotopes. There are about 7000 possible different radioactive isotopes.
The Nuclear Landscape
LET’S EXPLORE SOME PROPERTIES OF RADIOACTIVITY
Each type of radiation is ionizing but each has different properties which affect the hazards they pose, the detection mechanism and the shielding required to stop them.
Five Common Types
Alpha Decay
Beta Decay
Gamma Decay
Fission
Neutron Emission
ALPHA PARTICLE RADIATION
The daughter might also be radioactive and emit a second alpha particle. This is called a decay chain and is pretty common for heavy nuclei.
DECAY CHAINS
PuU
Th
Ra
Rn
Po
Pb
Hg
Au
BETA PARTICLE RADIATION
GAMMA-RAY RADIATION
FISSION
The heavy parent nucleus fissions …
… into two lighter (radioactive) fission fragment nuclei plus some left over neutrons
Sometimes a very heavy nucleus will fall apart before it can emit an alpha particle.
Fission can release an enormous amount of energy and is utilized in power plants and fission bombs.
NEUTRON EMISSION
Neutron emission doesn’t happen naturally because a neutron has no charge, so it has no barrier to overcome!
A nucleus is made up of nucleons (protons and neutrons):
Mass Spin Charge
Proton 938.272 MeV/c2 1/2 +1e
Neutron 939.565 MeV/c2 1/2 0
size: ~1 fm
In a nucleus, nucleons attract each other via the strong force ( range ~ 1 fm)
neutron proton(or any other charged particle)
V
r
R
V
rR
Coulomb Barrier Vc
R
eZZVc
221
Pote
nti
al
Pote
nti
al
…
…
Nucleons in a Box:Discrete energy levels in nucleus
R ~ 1.3 x A1/3 fm
WHAT HOLDS A NUCLEUS TOGETHER?
HOW UNSTABLE IS A RADIOACTIVE ATOM? The “Half-Life” describes how quickly Radioactive Material
decays away with time.
It is the time required for half of the unstable atoms to decay.
Some Examples: Some natural isotopes (like uranium and thorium) have
half-lives that are billions of years, Most medical isotopes (like Technicium-99m) last only a
few days
ELECTRONS, NEUTRONS AND PROTONS ARE FERMIONS (SPIN = HALF-INTEGER)
Electron (intrinsic spin = ½) + Orbital angular momentum (quantized) =
Total angular momentum
Also gives rise to magnetic moment
And ‘spin-orbit’ splitting
PROPERTIES OF IRON ISOTOPES
Z A AtomicMass (u)
NuclearMass(Ge
V/c2
Binding Energy(
MeV)Spin Natural
Abund. Half-life Decay QMeV
26 54 53.9396
13 50.2315 471.77 0 0.059 stable ... ...
26 55 54.9382
96 51.1618 481.07 3/2 ... 2.7y EC 0.23
26 56 55.9349
39 52.0902 492.26 0 0.9172 stable ... ...
26 57 56.9353
96 53.0221 499.91 1/2 0.021 stable ... ...
26 58 57.9332
77 53.9517 509.96 0 0.0028 stable ... ...
26 60 59.9340
77 55.8154 525.35 0 ... 1.5My b- 0.24
mp = proton mass, mn = neutron mass, m(Z,N) = mass of nucleus with Z,N
2),( BcNmZmNZm np
Most tables give atomic mass excess in MeV (so for 12C: =0):
Masses are usually tabulated as atomic masses
2/ cAmm u
Nuclear Mass~ 1 GeV/A
Electron Mass511 keV/Z
Electron Binding Energy13.6 eV (H)to 116 keV (K-shell U) / Z
m = mnuc + Z me + Be
MASS OF AN ATOM OR NUCLEI
M(Z,N) – Zmp – Nmn is known as the nuclear binding energy
Magic numbers:
Nuclei are more stable if the proton or neutron number is magic; doubly magic is most stable, e.g. 4He, 208Pb
NUCLEI HAVE SHELL STRUCTURE184
126
82
50282082
MARIA GOEPERT-MAYER While working at Argonne National
Laboratory in 1948, physicist Maria Goeppert Mayer developed the explanation of how neutrons and protons within atomic nuclei are structured. Called the "nuclear shell model," her work explains why the nuclei of some atoms are more stable than others and why some elements have many different atomic forms, called "isotopes," while others do not. For this work, she shared the 1963 Nobel Prize in physics.
Goeppert Mayer was only the second woman to receive the Nobel Prize in physics, following Marie Curie, and only the fourth American woman to win a Nobel Prize.
NUCLEI ALSO ACT LIKE A LIQUID DROP
The factors that determine whether the drop is ‘stable’ include Volume (Z+N) Surface energy (Z+N) Asymmetry (N/Z)
The combination of liquid drop energy (macroscopic) and effect of shell structure (microscopic) determine the binding energy of a nucleus
WHY DOES A RADIOACTIVE NUCLEUS DECAY? Think back to chemistry
A chemical reaction could be exothermic (generate energy) Endothermic (require energy to make it work)
Nuclear reactions or decays are the same A B + C
Q-value = energy generated by reaction = (mB + mC – mA)c2 (E = mc2) If Q > 0, energy is generated and decay may happen If Q < 0, energy is consumed
Example: Reaction Q
d p + n = 2. – 1. -1. =
d 14.003241982(27)
n 10.0129370(4)
p 14.0030740052(9)
4.0026032497(10)
Mass Table (u)
Decay of A in B and C is possible if reaction A B+C has positive Q-value
BUT: there might be a barrier that prolongs the lifetime
Decay is described by quantum mechanics and is a pure random process, with a constant probability for the decay to happen in a given time interval.
N: Number of nuclei A (Parent)l : decay rate (decays per second and parent nucleus)
NdtdN therefore ttNtN e)0()(
lifetime =1/t lhalf-life T1/2 = t ln2 = ln2/l is time for half of the nuclei present to decay
WILL A NUCLEUS WITH Q > 0 DECAY?
V
rR
Coulomb Barrier Vc
R
eZZVc
221
Pote
nti
al
unboundparticle
Example: for 197Au -> 58Fe + 139I has Q ~ 100 MeV ! yet, gold is stable.
most common: • b decay• n decay• p decay• a decay• fission
THE COULOMB BARRIER
For anything other than a neutron (or a neutrino) emitted from the nucleusthere is a Coulomb barrier The particle has to ‘tunnel’
through the barrier if it doesn’t have enough energy to get over the top
If that barrier delays the decay beyond the lifetime of the universe (~ 14 Gyr)we consider the nucleus as being stable.
not all decays that are energetically possible happen
In the middle of the chart, most nuclei beta decay:
Z
N
blue: neutron excessundergo b- decay:
AZ A(Z+1) + b- + +
red: proton excessundergo b+ decay:
AZ A(Z-1) + b+ + +
isobaric chain
b+ decay
electron capture
b- decay
p n + e+ + ne
e- + p n + ne
n p + e- + ne
Electron capture (or EC) of atomic electrons or, in astrophysics, of electrons in the surrounding plasma
BETA DECAY ENERGETICS
b decay basically no barrier -> if energetically possible it usually happens(except if another decay mode dominates)
therefore: any nucleus with a given mass number A will be converted into the most stable proton/neutron combination with mass number A by b decays
valley of stability(Bertulani & Schechter)
When no more neutrons can be bound, the neutron drip line is reached
Neutron drip line:
Sn= 0
beyond the neutron drip line, neutron decay occurs:
(Z,N) (Z,N-1) + n
Q-value: Qn = m(Z,N) - m(Z,N-1) - mn
beyond the drip line Sn<0
Neutron Separation Energy Sn
Sn(Z,N) = m(Z,N-1) + mn - m(Z,N) = -Qn for n-decay
As there is no Coulomb barrier, and n-decay is governed by the strong force,for our purposes the decay is immediate and dominates all other possible decay modes
the nuclei are neutron unbound
Neutron drip line very closely resembles the border of nuclear existence !
NEUTRON DECAY
30 40 50 60 70 80 90 100neutron num ber N
-5
0
5
10
15
20S
n (M
eV)
Example: Neutron Separation Energies for Z=40 (Zirconium)
neutron drip line
valley of stability
add 37 neutrons
At Michigan State Univ, the National Superconducting Cyclotron Lab (NSCL) is exploring the limits of nuclear stability by trying to reach neutron drip line through fragmenting Uranium nuclei.
neutrons
protons
Mass knownHalf-life knownnothing known
H(1)
Fe (26)
Sn (50)
Pb (82)
neutron dripline
proton dripline
note odd-even effect in drip line !(p-drip: even Z more bound - can take away more n’s)(n-drip: even N more bound - can take away more p’s)
ALPHA DECAY
yelloware a emitter
Nuc le a r C ha rg e Yie ld in Fissio n o f 234U
25 30 35 40 45 50 55 60 65
80 100 120 140 160 M a ss Num b e r A
Pro to n Num b e r Z
0
5
10
15
20
Yie
ld Y
(Z
) (%
)
FISSION
green = spontaneous fission