Download Atoms, nuclei, particles

Atoms, nuclei, particles
Nikolaos Kidonakis
Physics for Georgia Academic Decathlon
September 2016
Age-old questions
• What are the fundamental particles of matter?
• What are the fundamental forces of nature?
• What is the Universe made of ?
Atomic Models
Ancient Greece
Demokritos - early atomic theory
Atom - indivisible
Modern times
J.J. Thomson: electron; plum pudding model of the atom
Rutherford - scattering experiments
deflection of alpha particles striking gold foil
heavy positively charged nucleus
Bohr model of the atom - early Quantum Mechanics
Quantum mechanics → wave-particle duality
Probing particles such as electrons and protons at high energies required
to resolve subatomic and subnuclear distance scales
de Broglie wavelength of a probing particle defines the minimum object size
that can be resolved λ = h/p
with current collider energies we can “see” down to 10−19 m
Atoms, nuclei, nucleons, and quarks
Foundations of Modern Physics
Special and General Relativity
Albert Einstein
Spacetime - time dilation - length contraction
E = mc2
Gravity - curved spacetime
Foundations of Modern Physics
Quantum Mechanics
Werner Heisenberg
Erwin Schrodinger
Paul Dirac
Heisenberg uncertainty principle and formalism
Schrodinger equation
Dirac equation - relativistic QM - antimatter
Quantum mechanics is the reality of all nature and is especially essential
for understanding the atomic and subatomic world
Without QM atoms could not exist → no chemistry
Classically accelerating charges radiate electromagnetic radiation
- electrons would spiral into the nucleus
Early quantum mechanics
Planck: quanta of energy E = hf
Planck’s constant: h = 6.626 × 10−34 J s
Einstein: photons
Bohr model of the atom
heavy nucleus surrounded by electrons (planetary model)
Bohr postulate: angular momentum of electron is quantized
L = nh̄
with
n = 1, 2, 3, ...
where h̄ = h/(2π)
For an electron of mass m, speed v, and distance r from the nucleus,
L = mvr, so
mvr = nh̄ ⇒ v =
nh̄
mr
Consider nucleus with Z protons
Then, centrifugal force equals electric force of attraction
h̄2 n2
kZe2
mv 2
⇒ rn =
=
r
r2
mke2 Z
Then energy levels are also quantized
kZe2
mk 2 e4 Z 2
E1
E=−
⇒ En = −
=
2r
n2
2h̄2 n2
For hydrogen atom Z = 1 and E1 = −13.6 eV
Emission of photons-spectral lines
E = Eni − Enf ⇒
hc
= E1
λ
Then
1
=R
λ
1
1
−
n2i
n2f
with Rydberg constant R = 1.097 × 107 m−1
1
1
−
n2i
n2f
Heisenberg uncertainty principle
∆x ∆px ≥
h̄
2
∆E ∆t ≥
h̄
2
where h̄ = h/(2π)
fundamental indeterminacy in simultaneous knowledge of observables
Schrodinger equation
one-dimensional version
dψ
h̄2 d2 ψ
+
U
ψ
=
ih̄
−
2m dx2
dt
Time-independent equation
h̄2 d2 ψ
−
+ U ψ = Eψ
2
2m dx
Pauli exclusion principle: no two fermions can have all quantum numbers
be identical
Shell structure in atoms
Dirac equation
incorporate special relativity in quantum mechanical description
ih̄γ µ ∂µ ψ = mcψ
electron spin
prediction of antiparticles
Quantum Field Theory and the Standard Model of particle physics
QM+Special Relativity → QFT
Particles represented by quantum fields
Fundamental matter particles: quarks, leptons + antiparticles
Fundamental forces: gravity, electromagnetic, weak, strong
Force mediators: gluons, photon, W ± , Z
Higgs boson: generates mass
Quantum Chromodynamics (QCD) + ElectroWeak Theory
Nucleus
A=Z+N
A: atomic mass number, i.e. number of nucleons (protons and neutrons)
Z: atomic number, i.e. number of protons
N: number of neutrons
isotopes
Atom is mostly “empty” space
atom size ∼ 1 Å=10−10 m
nucleus size ∼ 1 fm=10−15 m
strong nuclear force holds nucleons together;
compensates for electric repulsion among protons
liquid-drop model: approximate nucleus as sphere with uniform
density that drops to zero at surface
M c2 = Zmp c2 + N mn c2 + B
where B is the binding energy
Decays
α-decay
238
92 U
4
→ 234
90 Th + 2 He
β decay
n → p + e− + ν̄e
γ decay
transition between states
Nuclear shell model
Half life
radioactive decays occur randomly
dN
= −λN
dt
with λ the decay constant
Then, if we start with N0 nuclei, after time t we have
N = N0 e−λ t
half-life τ is time for half of the nuclei to disintegrate
ln 2
N0
= N0 e−λ τ ⇒ τ =
2
λ
Fission
Heavier nuclei are unstable
235
92 U
1
92
+ 10 n → 141
56 Ba + 36 Kr + 3 0 n
235
92 U
1
94
+ 10 n → 140
54 Xe + 38 Sr + 2 0 n
Chain reaction:
if m neutrons are produced and E0 is the energy released in each fission,
then the energy released in the jth generation is E0 mj
Fusion
1
1H
+ 11 H → 21 H + e+ + νe
2
1H
3
2 He
Stellar nucleosynthesis
+ 11 H → 32 He + γ
+ 32 He → 42 He + 2 11 H + γ