Atoms, nuclei, particles

Transcription

1 Atoms, nuclei, particles Nikolaos Kidonakis Physics for Georgia Academic Decathlon September 2016

2 Age-old questions What are the fundamental particles of matter? What are the fundamental forces of nature? What is the Universe made of?

3 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

4 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 m

5 Atoms, nuclei, nucleons, and quarks

6 Foundations of Modern Physics Special and General Relativity Albert Einstein Spacetime - time dilation - length contraction E = mc 2 Gravity - curved spacetime

7 Foundations of Modern Physics Quantum Mechanics Werner Heisenberg Erwin Schrodinger Paul Dirac Heisenberg uncertainty principle and formalism Schrodinger equation Dirac equation - relativistic QM - antimatter

8 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 Planck: quanta of energy E = hf Early quantum mechanics Planck s constant: h = J s Einstein: photons

9 Bohr model of the atom heavy nucleus surrounded by electrons (planetary model) Bohr postulate: angular momentum of electron is quantized where h = h/(2π) L = n h with n = 1,2, 3,... For an electron of mass m, speed v, and distance r from the nucleus, L = mvr, so mvr = n h v = n h mr Consider nucleus with Z protons Then, centrifugal force equals electric force of attraction mv 2 r = kze2 r 2 r n = h2 n 2 mke 2 Z

10 Then energy levels are also quantized E = kze2 E n = mk2 e 4 Z 2 2r 2 h 2 n = E 1 2 n 2 For hydrogen atom Z = 1 and E 1 = 13.6 ev Emission of photons-spectral lines Then E = E ni E nf hc λ = E 1 1 λ = R ( 1 n 2 i 1 n 2 f with Rydberg constant R = m 1 ( 1 ) n 2 i 1 n 2 f )

11 Heisenberg uncertainty principle x p x h 2 where h = h/(2π) E t h 2 fundamental indeterminacy in simultaneous knowledge of observables

12 one-dimensional version Schrodinger equation h2 2m d 2 ψ + Uψ = i hdψ dx2 dt Time-independent equation h2 2m d 2 ψ + Uψ = Eψ dx2 Pauli exclusion principle: no two fermions can have all quantum numbers be identical Shell structure in atoms

13 Dirac equation incorporate special relativity in quantum mechanical description i hγ µ µ ψ = mcψ electron spin prediction of antiparticles

14 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

15 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

16 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 where B is the binding energy Mc 2 = Zm p c 2 + Nm n c 2 + B

17 Decays α-decay U Th + 4 2He β decay n p + e + ν e γ decay transition between states Nuclear shell model

18 Half life radioactive decays occur randomly with λ the decay constant dn dt = λn Then, if we start with N 0 nuclei, after time t we have N = N 0 e λ t half-life τ is time for half of the nuclei to disintegrate N 0 2 = N 0 e λ τ τ = ln 2 λ

19 Fission Heavier nuclei are unstable U + 1 0n Ba Kr n U + 1 0n Xe Sr n Chain reaction: if m neutrons are produced and E 0 is the energy released in each fission, then the energy released in the jth generation is E 0 m j

20 Fusion 1 1H + 1 1H 2 1H + e + + ν e 2 1H + 1 1H 3 2He + γ 3 2He + 3 2He 4 2He H + γ Stellar nucleosynthesis