Nuclear Basics Summer 2010
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Transcript of Nuclear Basics Summer 2010
Basic Nuclear Physics
Roppon Picha
created: November 2005updated: April 8, 2010
Dalton’s atoms (1808)
J.J. Thomson’s Experiment
cathode rays = electrons (1897)
Rutherford, Geiger, Marsden
22688 Ra → 222
86 Rn +α → α + 21884 Po
rate of alpha scattering at angle θ from nucleus of chargeZ :
R(θ) ∝(
Ze2
mαv2α
)2 1sin4(θ/2)
Electron configuration
Rutherford model (1911): Electrons orbit the nucleus likeplanets orbit the Sun.
Bohr model of the atom (1913): Electrons stay in theatom on special orbits (orbitals).
Experimentally verified by James Franck and GustavLudwig Hertz in 1914. Atoms only absorb certain“chunks” of energy.
Electron configuration
principal quantum number: n = 1,2,3, . . .
e− most strongly bound at n = 1.
example: sodium (Na) has 11 electrons. In ground state,2 electrons are in n = 1 level, 8 in n = 2, and 1 in n = 3.
Hydrogen
V (r) = − e2
4πε0
1r
En = −13.6n2 eV
(Bohr formula, 1913)
hydrogenic (1 electron, Ze nuclear charge):
En = −13.6Z 2
n2
Sub configurations
Besides n, we have orbital angular momentumquantum number l .
l = 0,1,2, . . . ,n − 1letters: s, p, d, f, g, h, . . .
Then, there is spin quantum number s.
Quantum angular momentum
total angular momentum quantum number j :
j = s + l
values jump in integer steps:
|l − s| ≤ j ≤ l + s
Quantum angular momentum
example:for the electron, s = 1/2. if l = 1, what are possible valuesof j?
s = 1/2 and l = 3?
What are all possible j values for electron in n = 4 level?
Proton (1919) was discovered by Rutherford.
α+ N → H + O
Protos = first
Chadwick’s Neutron Discovery
• Existence suggested since 1920 by Rutherford.• Finally found via experiments in 1932.
94Be5 +4
2 He2+2 −→ 12
6 C +10 n1
or (α, n) reaction
mass: neutron 939.6 MeV/c2 ≈ proton 938.3 MeV/c2
Neutron energy
Fast neutrons = high-energy neutrons. E > 1 eV.
Thermal neutrons = those with average thermal energycorresponding to room temperature (T = 300 K).
Eth =32
kBT ≈ 140
eV
where kB = 1.38× 10−23 J/K.
Energy and Velocity
For a nucleon of kinetic energy 15 MeV, the velocity canbe calculated via
T =12
mv2
v =
√2Tm
≈ c
√2 · 15938
≈ 0.18c
de Broglie wavelength of this nucleon is
λ =h
mv=
4.1× 10−21 MeV s938MeV c−2 · 0.18c
≈ 7.3 fm
Accelerated Charge
EM radiation
Electric field far away does not know of particle’smovement.
The electric field form a wavefront consisting radial(Coulomb) and transverse components.
radiated power = P =q2a2
6πε0c3 Larmor’s equation
Electromagnetic Spectrum
p++
Region of Stability
Binding Energy per Nucleon
Binding energy
binding energy of most nuclei ∼ 8 MeV/nucleon
electrons are bound at ∼ 10 eV to atoms.
Separation Energy
removing a proton:
AZ XN −→ A−1
Z−1YN
removing a neutron:
AZ XN −→ A−1
Z YN−1
Separation energy (S) is the difference between bindingenergies (B) of initial nucleus and final nucleus.
Separation Energy
S > 0 when we change a stable nucleus (high B) into aless stable nucleus (low B).
B = (∑
mconstituents −matom)c2
S ≡ Bi − Bf
Sp = B(AZ XN)− B(A−1
Z−1YN)
Sn = B(AZ XN)− B(A−1
Z YN−1)
Ionization vs. Separation
Quantum behaviors
Subatomic particles can be described by quantummechanics.
States are represented by wave function ψ(x , t).
Particles = Wave packets = superpositions of waves.
Wave functions
Wave = non-localized state.
∆x ·∆p > ~
(Heisenberg uncertainty relation)
To get the wave function and its evolution, solveSchrodinger’s equation:
i~∂ψ
∂t=
(− ~2
2m+ V
)ψ
Wave function
Normalization: ∫ ∞
−∞|ψ(x , t)|2 dx = 1
At any given time, the particle has to be somewhere.
expectation values:
〈x〉 =
∫ψ∗(x)ψ dx
〈p〉 =
∫ψ∗(p)ψ dx
Wave properties
de Broglie wavelength of a (non-zero mass) particle ofmomentum p
λ =hp
Experimental verification: Davisson and Germer (1954).
Davisson and Germer used 54-eV electron beam toscatter of a nickel crystal. An interference peak wasobserved, similar to Bragg peak in x-ray diffraction.
Photons
∼ 1900: Blackbody radiation study led Planck to thinkabout nature of electromagnetic energy.
1905: Einstein proposed that light consists of photons,each possessing a certain lump of energy.
Total energy = multiples of this number.
Energy
Planck-Einstein relation gives energy of a photon:
E = hν = ~ω =hcλ
ν and ω are frequency and angular frequency,respectively.
Energy
h = 6.63× 10−34 J s = 4.14 eV s
for λ given in angstrom:
E =12.4λ
keV
Characteristic radiation of atoms which has only certainvalues are due to the fact that the atoms only exist incertain stable states of discrete energies.
Photon interactions
excitation (and de-excitation)
hν + Am ↔ An
ionization (and recombination)
hν + A ↔ A+ + e−
Fermions and Bosons
Protons, neutrons, and electrons belong to the fermionfamily.
Quarks and leptons are also fermions.
They have odd half-integer spins: s = 1/2,3/2,5/2, . . ..
Bosons have integer spin: s = 0,1,2, . . ..examples: photons (s = ±1) and 4He atoms (s = 0)
Periodic table
Electrons are identical fermions. At a given orbital(n, l ,m), only two electrons can occupy the same state(one spin-up, one spin-down)
For each l , there are 2l + 1 values of ml . For each (l ,ml ,there is two spin states (ms = ±1
2 ).
Exercise: What are maximum number of electrons forl = 0,1,2,3?
Periodic table shows an integer increase of protons andelectrons. Shells are filled, from low to high energies.
Ground-state configs:
• H: (1s1)
• He: (1s2)
• Li: (He)(2s1)
• Be: (He)(2s2)
• B: (He)(2s2)(2p1)
• . . .
information about a radioisotope.
Decay Law
dN(t)dt
= −λN(t)
t is time. N(t) is number of nuclei. λ is decay constant.solution:
N(t) = N0e−λt
N0 = number of nuclei at the starting time.decay constant is inversely proportional to the half-life:
λ =ln 2t1/2
A parent nuclide decays and yields a daughter nuclide.
increase in number of daughter (D) = decrease in numberof parents (P)
Df − Di = Pi − Pf
Decay constant
Decays aren’t always 1-to-1:
A → B (55% of the time)→ C (40%)→ D (5%)
For branched decays, the total decay constant is just thesum of each mode constant:
λtot = λ1 + λ2 + λ3 + . . .
Lifetime
For a given decay constant λ, the lifetime of the state is
τ =1λ
It is the time taken the state to drop from N0 toN0/e ≈ 0.37N0.
branched decays:
τ =1
λ1 + λ2 + . . .
Activity
A ≡ −dNdt
= λN = −λN0e−λt = A0e−λt
A is also called “decay rate” or “disintegration rate.”
units: becquerel (1 s−1) or curie (3.7× 1010 s−1)
Mysterious rays
Henri becquerel discovered radioactivity from uranium orein 1896.
At Cambridge, Rutherford studied these unknown raysand published results in 1899.
Those that got absorbed by a sheet of paper or a few cmof air was named alpha rays.
The more penetrating ones were called beta rays.
Alpha Decay
Alpha (α) = 2p&2n bound state
Process:AZ XN −→ A−4
Z−2YN−2 + 42He2
Examples:
22688 Ra138 → 222
86 Rn136 + α23892 U146 → 234
90 Th144 + α
mX c2 = (mY c2 + TY ) + (mαc2 + Tα)
Q ≡ (mi −mf )c2 = (mX −mY −mα)c2
Alpha emitters with large Q tend to have short half-lives.
lnλ(E) = a− bZ√E
Geiger-Nuttall law. λ is the decay constant; a and b areconstants; Z is the atomic number; E is the decay energy.
Beta Decay
W. Pauli: There must be a neutrino. (1930)Cowan and Reines observed it. (1956)
Beta Decay
Processes:
n → p + e− + ν̄e β− decayp → n + e+ + νe β+ decay (rare)
p + e− → n + νe e capture (ε)
Examples:
23490 Th144 → 234
91 Pa143 + e− + ν̄e53m27 Co → 53
26Fe + e+ + νe15O + e− → 15N + νe
X-ray
Charged particles that decelerate create electromagneticradiation. This process is known as bremsstrahlung.
Photons can excite or ionize atoms.
Subsequent atomic transitions can produce additionalX-ray photons. This process is called X-rayfluorescence.
If an atomic electron absorbs such X-ray photon, it can beejected. These electrons are called Auger (oh-zhay)electrons.
Gamma Decay
A year after Rutherford discovered α and β rays, PaulVillard discovered a more penetrating radiation fromradium. This is the gamma (γ) ray.
Excited nuclear states can decay via γ emission. Typicalenergies ∼ 0.1− 10 MeV.
Examples:
99m43 Tc → 99
43Tc + γ isomeric transition6027Co → 60
28Ni + e− + ν̄e + γ with β−
Internal conversion
An excited nucleus can interact with an orbital electron,transferring energy Eex .
The electron gets ejected with energy
Ee = Eex − Eb
where Eb is the binding energy of the electron.
The gamma decay and internal conversion decaycontribute to total decay probability:
λ = λγ + λe
Radiation Units
quantity description units
activity (A) decay rate curie (Ci), becquerel (Bq)exposure (X ) air ionization roentgen (R), coulomb/kgabsorbed dose (D) absorbed energy rad, gray (Gy)dose equivalent (DE) bio. effects rem, sievert (Sv)
Quiz
1. What kind of radiation does not come from anucleus? [choices: α, β, x-ray, γ]
2. Be-7 decays by capturing an electron. What is theresulting nuclide?
3. 15.1% of natural samarium is 147Sm, which decays byemitting α. 10 grams of natural samarium gives 120 αper second. Calculate activity per gram of 147Sm.
Reaction Cross Section
for reactiona + X −→ Y + b
σ =reaction rate
fluxincident · densitytarget
=rate of detecting b
(flux of a) · (X areal density)
Nuclear Reactions: First reaction in lab
Creating new nuclides
making light radionuclides:
14N + n →14 C +1 H55Mn +2 H →55 Fe + 2n
59Co + n →60 Co + γ
making Np-239 (transuranic)
238U + n →239 U239U →239 Np + e− + ν̄e
Balancing nuclear equations
What is x in each of these nuclear reactions?
19779 Au +12
6 C → 20685 At + x
3216S +4 He → x + γ
2713Al + p → x + n
4He +177 N → x +1 H
EM interactions
Main processes:
Photoelectric absorption
Compton scattering
Pair production
Intensity attenuation:
I(x) = I(0)e−µx
half-value layer = thickness that reduces intensity by 50%.
Producing radionuclides
Ways to do it:
• Reactors• Accelerators• Generators
Reactors
AX + n → →
Longer irradiation time → higher specific activity.
Examples:
13051 Te + n → →
63Li + n → α+ t
as fission products:
8536Kr, 133
54 Xe, 9038Sr, 99
42Mo, 13755 Cs
Accelerators
Usual projectiles: p, d , α
Examples:
2010Ne(d , α) 18
9 F7634Se(p,n) 76
35Br3517Cl(α, n) 38
19K
Generators
Suppose you want to use a short-lived nuclide producedfrom a reactor. But you are far away from the reactor.What can you do?
Prepare the parent nuclide which has longer half-life, in adevice that can separate the daughter from the parent.
Examples:4422Ti (t1/2 = 6 y) ⇒ 44
21Sc (t1/2 = 3.9 h)8337Rb (86 d) ⇒ 83m
36 Kr (1.8 h)9942Mo (66 h) ⇒ 99m
43 Tc (6 h)
the End