Modern Physics

1. Max Planck proposed that an atom can absorb or emit energy only in chunks known as quanta. • The energy, E ,of each quantum depends on the frequency of the radiation E= hf h= 6.626 x 10-34 J·s (Planck’s constant) • Einstein suggested that a fundamental property of electromagnetic radiation consists of quanta of energy known as photons. E = hf= hc/λ Modern Physics

2. “Light particle” Before Collision After Collision Photo-Electric Effect • In this “quantum-mechanical” picture, the energy of thelight particle (photon) must overcome the binding energy of the electron to the nucleus. • If the energy of the photon exceeds the binding energy, theelectron is emitted with a KE = Ephoton – Ebinding. Einstein used the photon hypothesis to explain the Photoelectric effect ( emission of electrons from a metal surface when a light is incident on it)

3. The Electromagnetic Spectrum Shortest wavelengths (Most energetic photons) E = hn = hc/l h = 6.6x10-34 [J*sec](Planck’s constant) Longest wavelengths (Least energetic photons)

4. There is a threshhold negative potential, the stopping potential, V0 , below which no current will flow into the circuit Each light intensity has a maximum current flow, but the stopping potential remains the same

5. When V is negative, only electrons with a kinetic energy greater than |eV0| can reach the anode, the maximum kinetic energy is given by eV0. • ( ½ mv2 )max = eV0 = hf –φ • φ = work function ( energy needed to release an electron from the metal)

6. Special relativity - the laws of physics are same in all inertial frames of reference • Invariance of c - the speed of light in a vacuum is a universal constant ( c ) which is independent of the motion of the light source Special relativity

7. Lorentz contraction • An observer moving with respect to an object will observe it to be contracted along the direction of motion by the factor • A perceived reduction in the length of an object • Negligible at the speeds we experience everyday but would be noticeable at velocities comparable to that of light For more information see http://www.fourmilab.ch/cship/lorentz.html • Time dilation • The time lapse between two events is dependent on the relative speeds of the observer’s reference frames

8. Thetotal energy of a mass m moving at a velocity v is given by • So when v = 0 , E= mc2 Einstein’s mass-energy equivalence

9. αAlpha particles are produced from the radioactive decay of heavy elements such as uranium. They are composed of two neutrons and two protons identical to the nucleus of a helium atom. Because of their relative size and electrical charge from the two protons, alpha particles can travel only a very short distance in any material. For example a normal sheet of paper can stop alpha particles. Alpha, Beta, & gamma radiation βBeta particles are electrons that come from transformation of a neutron in the nucleus of an atom to a proton. They can travel up to about five meters in air and one centimeter in tissue. gGamma rays are electromagnetic radiation similar to X-rays. Unlike the latter, which are produced by machines, gamma rays are emitted from the nucleus of a radioactive atom that is in an excited state. Gamma rays travel at the speed of light and can penetrate long distances in air and tissue. Several centimeters of lead or meters of water are needed to stop typical gamma rays

10. a decay - involves strong and coloumbic forces - alpha particle and daughter nucleus have equal and opposite momentums (i.e. daughter experiences “recoil”)

11.  decay - three types 1) - decay - converts one neutron into a proton and electron - no change of A, but different element - release of anti-neutrino (no charge, no mass) 2) + decay - converts one proton into a neutron and electron - no change of A, but different element - release of neutrino 3) Electron capture

12. g decay - conversion of strong to coulombic E - no change of A or Z (element) - release of photon - usually occurs in conjunction with other decay Spontaneous fission - heavy nuclides split into two daughters and neutrons - U most common (fission-track dating) Fission tracks from 238U fission in old zircon

13. Nuclear fission

14. The time it takes for one half of the sample to decay Half Life

15. Activity calculations - usually reported in dpm (disintegrations per minute), example: 14C activity = 13.56 dpm / gram C - because activity is linerarly proportional to number N, then A can be substituted for N in the equation Example calculation: How many 14C disintegrations have occurred in a 1g wood sample formed in 1804AD? T=200y t1/2 = 5730y so l = 0.693/5730y = 1.209e-4 y-1 N0=A0/l so N0=(13.56dpm*60m/hr*24hr/day*365days/y) /1.209e-4= 5.90e10 atoms N(14C)=N(14C)0*e-(1.209e-4/y)*200y = 5.76e10 atoms # decays = N0-N = 2.4e9 decays

16. Heisenberg’s uncertainty Principle

17. Models of the Atom a Historical Perspective

18. fire Democritus earth air water Aristotle • 400 B.C. - Democritus thought matter could not be divided indefinitely. • This led to the idea of atoms in a void. • 350 B.C - Aristotle modified an earlier theory that matter was made of four “elements”: earth, fire, water, air. Early Greek Theories • Aristotle was wrong. However, his theory persisted for 2000 years.

19. 1800 -Dalton proposed a modern atomic model based on experimentation not on pure reason. • All matter is made of atoms. • Atoms of an element are identical. • Each element has different atoms. • Atoms of different elements combine in constant ratios to form compounds. • Atoms are rearranged in reactions. John Dalton • His ideas account for the law of conservation of mass (atoms are neither created nor destroyed) and the law of constant composition (elements combine in fixed ratios).

20. Dalton’s “Billiard ball” model (1800-1900) Atoms are solid and indivisible. Materials, when rubbed, can develop a charge difference. This electricity is called “cathode rays” when passed through an evacuated tube (demos). These rays have a small mass and are negative. Thompson noted that these negative subatomic particles were a fundamental part of all atoms. Adding Electrons to the Model • Thompson “Plum pudding” model (1900) • Negative electrons in a positive framework. • The Rutherford model (around 1910) • Atoms are mostly empty space. • Negative electrons orbit a positive nucleus.

21. Zinc sulfide screen Thin gold foil Lead block Radioactive substance path of invisible -particles Rutherford shot alpha () particles at gold foil. Most particles passed through. So, atoms are mostly empty. Some positive -particles deflected or bounced back! Thus, a “nucleus” is positive & holds most of an atom’s mass. Ernest Rutherford

22. Electrons orbit the nucleus in “shells” • Electrons can be bumped up to a higher shell if hit • by an electron or a photon of light. Bohr’s model There are 2 types of spectra: continuous spectra & line spectra. It’s when electrons fall back down that they release a photon. These jumps down from “shell” to “shell” account for the line spectra seen in gas discharge tubes (through spectroscopes).

23. Quantum Numbers: • n= principal quantum number • l = azimuthal quantum number • (orbital angular momentum) • ml = magnetic quantum number • ms = spin magnetic quantum number Quantum Model

24. Quantum Mechanics and Atomic Orbitals • Orbitals and Quantum Numbers

25. Representations of Orbitals The s-Orbitals

26. Representations of Orbitals The p-Orbitals

27. d-orbitals

28. Many-Electron Atoms Electron Spin and the Pauli Exclusion Principle

29. The smallest pieces of matter… • Nuclear physics and particle physics study the smallest known building blocks of the physical universe -- and the interactions between them. • The focus is on single particles or small groups of particles, not the billions of atoms or molecules making up an entire planet or star.

30. Further layers of substructure: u quark: electric charge = 2/3 d quark: electric charge = -1/3 Proton = uud electric charge = 1 Neutron = udd electric charge = 0 www.cpepweb.org If each proton were 10 cm across, each quark would be .1 mm in size and the whole atom would be 10 km wide.

31. Introducing the neutrino Another subatomic particle, the neutrino, plays a crucial role in radioactive decays like n -> p+ + e- + ve - The ve(electron-neutrino) is closely related to the electron but has strikingly different properties.