PHYS 219 General Physics: Electricity, Light and Modern Physics

Transcription

1 PHYS 219 General Physics: Electricity, Light and Modern Physics Final exam is scheduled on Thursday May 8 10 AM In Physics 112 It will cover five Chapters 25, 27, 28, 29, and 30. Review lecture notes, home works, and recitation problems! FINAL EXAM: There will be a two-hour final exam. The final exam is multiple-choice (20 problems, ~4 problems per chapter). The times and locations of the evening exams are as follows: Final Exam : Thursday May 8 10 AM in Physics 112 All exams are closed book. For the exams you will need a #2 pencil, a calculator and your student ID. You may make a single crib sheet for Exam 1 (you may write on both sides of an 8.5 x 11 sheet of paper). Bring this and a second crib sheet to Exam 2; bring both crib sheets and a third to the Final Exam. Many, but not all, formulae will be provided on the front of the Exams.

2 Equation Sheet - Physics 219 Final Exam 8 c 3. 00x10 m / s c v c f vac c, f film v fn v / ( v / c) f n t min air 2n film h n 15 1 m d 2 2 n film 34 ev s J s 23 kb J / K t m 2d n min film air 4n t min 4n air coating w sin θ = ±m λ m = 1, 2, 3, t t 0 1 v / c 2 2 d sin θ = m λ m = 0, ±1, ±2, d sin θ = m d sin θ = (m + ½) λ m = 0, ±1, ±2, m = 0, ±1, ±2, Rayleigh' s Criterion L L0 1 v / c 2 2 v min OA 1.22 D vot vta 1 v v / c 2 OT TA p mv 0 1 v c 2 2 KE mc v / c 2 2 m c 0 2 TE KE m c 0 mc 2 0 1v 2 c 2 2

3 Equation Sheet - Physics 219 Final Exam (continued) W c hf KEelectron hf Wc c Ephoton hf hc p photon E hf h 2ck BT ( ) 4 c c ( ) 2 hc 2 5 hc/ kbt ( e 1) h p h 2 m( KE) xp h 4 Et h 4 L h n 2 r h 4 mke 2 2 n 2 2 E tot k e m 1 h n 2 2 E tot 13.6eV 2 n A X Z, A Z N 1/3 r r0 A r m N N e t T1/2 0 ln

4 Chapter 29 Atomic Theory Lecture Structure of the Atom: What s Inside? 29.2 Atomic Spectra 29.3 Bohr s Model of the Atom 29.4 Wave Mechanics and the Hydrogen Atom 29.5 Multielectron Atoms 29.6 Chemical Properties of the Elements and the Periodic Table 29.7 Applications 29.8 Quantum Mechanics and Newton s Mechanics: Philosophical Issues

5 Modern Quantum Mechanics Modern quantum mechanics depends on the ideas of wave functions and probability densities instead of mechanical ideas of position and motion To solve a problem in quantum mechanics, you use Schrödinger s equations The solution gives the wave function, including its dependence on position and time Four quantum numbers are required for a full description of the electron in an atom Bohr s model used only one Section 29.4

6 Quantum Numbers, Summary Section 29.4

7 Principle Quantum Number n is the principle quantum number It can have values n = 1, 2, 3, It is roughly similar to Bohr s quantum number As n increases, the average distance from the electron 2 to the nucleus increases 2 h r n 2 4 mke States with a particular value of n are referred to as a shell Section 29.4

8 Orbital Quantum Number l is the orbital quantum number Allowed values are l = 0, 1, 2, n - 1 The angular momentum of the electron (r p = r mv) is proportional to l States with l = 0 have no angular momentum See the table for shorthand letters for various l values Section 29.4

9 Orbital Magnetic Quantum Number and Spin Quantum Number Orbital Magnetic Quantum Number m is the orbital magnetic quantum number It has allowed values of m = - l, -l + 1,, -1, 0, 1, l You can think of m as giving the direction of the angular momentum of the electron in a particular state Spin Quantum Number s is the spin quantum number s = + ½ or ½ These are often referred to as spin up and spin down This gives the direction of the electron s spin angular momentum Section 29.4

10 Electron Shells and Probabilities A particular quantized electron state is specified by all four of the quantum number n, l, m and s The solution of Schrödinger s equation also gives the wave function of each quantum state ( r,, ) From the wave function, you can calculate the probability for finding the electron at different locations around the nucleus Plots of probability distributions for an electron are often called electron clouds nlm nlm ( r,, ) 2 s Section 29.4

11 Electron Clouds nlm ( r,, ) ( r nlm,, ) ( r,, ) s 2 ( r,, ) /2 a0 e ra / h r n mke r a nm 0 for n 1 (Bohr radius ) Section 29.4

12 Electron Cloud Example Ground state of hydrogen n = 1 The only allowed state for l is l = 0 This is an s state The only allowed state for m is m = 0 The allowed states for s are s = ± ½ The probability of finding an electron at a particular location does not depend on s, so both of these states have the same probability The electron probability distribution forms a spherical cloud around the nucleus ( r,, ) See fig A nlm ( r,, ) ( r,, ) /2 a0 s e ra / Section

13 Hydrogen Electrons, final The electron probability distributions for all states are independent of the value of the spin quantum number For the hydrogen atom, the electron energy depends only on the value of n and is independent of l, m and s This is not true for atoms with more than one electron Section 29.4

14 Multielectron Atoms The electron energy levels of multielectron atoms follow the same pattern as hydrogen Use the same quantum numbers The electron distributions are also similar There are two main differences between hydrogen and multielectron atoms (1) The values of the electron energies are different for different atoms (2) The spatial extent of the electron probability clouds varies from element to element Section 29.5

15 Pauli Exclusion Principle Each quantum state can be occupied by only one electron Each electron must occupy its own quantum state, different from the states of all other electrons This is called the Pauli exclusion principle Each electron is described by a unique set of quantum numbers Section 29.5

16 Electron Configuration There is a useful shorthand notation for showing electron configurations Examples: 1s 1 1 n =1 s l = 0 Superscript 1 1 electron No information about electron spin 1s 2 2s 2 2p 2 2 electrons in n = 1 with l = 0 2 electrons in n = 2 with l = 0 2 electrons in n = 2 with l = 1 Section 29.5

17 Filling Energy Levels The energy of each level depends mainly on the value of n In multielectron atoms, the order of energy levels is more complicated For shells higher than n = 2, the energies of subshells from different shells being to overlap In general, the energy levels fill with electrons in the following order: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f Section 29.5

18 Order of Energy Levels 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 4f Section 29.5

19 Chemical Properties of Elements Quantum theory explains the structure of the periodic table The periodic table was first assembled by Dmitry Mendeleyev in the late 1860 s Mendeleyev and other chemists had noticed that many elements could be grouped according to their chemical properties Mendeleyev organized his table by grouping related elements in the same column His table had a number of holes because many elements had not yet been discovered Section 29.6

20 Chemical Properties, cont. Mendeleyev could not explain why the regularities in the periodic table occurred The electron energy levels and the electron configuration of the atom are responsible for its chemical properties When an atom participates in a chemical reaction, some of its electrons combine with electrons from other atoms to form chemical bonds The bonding electrons are those occupying the highest energy levels Section 29.6

21 Structure of the Periodic Table Mendeleyev grouped elements into columns according to their common bonding properties and chemical reactions These properties rely on the valence electrons and can be traced to the electron configurations The rows correspond to different values of the principle quantum number, n Since the n = 1 shell can hold only two electrons, the row contains only two elements The number of elements in each row can be found by using the rules for allowed quantum numbers Section 29.6

22 Periodic Table Section 29.6

23 Periodic Table

24 Example Electron Configurations Section 29.6

25

26 Electrons and Shells The electron that forms bonds with other atoms is a valence electron When a shell has all possible states filled it forms a closed shell Elements in the same column in the periodic table have the same number of valence electrons The last column in the periodic table contains elements with completely filled shells These elements are largely inert They almost never participate in chemical reactions Section 29.6

27

28 Atomic Clocks Atomic clocks are used as global time standards The clocks are based on the accurate measurements of certain spectral line frequencies Cesium atoms are popular One second is now defined as the time it takes a cesium clock to complete 9,192,631,770 ticks Section 29.7

29 Incandescent Light Bulbs The incandescent bulb contains a thin wire filament that carries a large electric current Type developed by Edison The electrical energy dissipated in the filament heats it to a high temperature The filament then acts as a blackbody and emits radiation Section 29.7

30 Fluorescent Bulbs This type of bulb uses gas of atoms in a glass container An electric current is passed through the gas This produces ions and high-energy electrons The electrons, ions, and neutral atoms undergo many collisions, causing many of the atoms to be in an excited state These atoms decay back to their ground state and emit light Section 29.7

31 Lasers Lasers depend on the coherent emission of light by many atoms, all at the same frequency In spontaneous emission, each atom emits photons independently of the other atoms It is impossible to predict when it will emit a photon The photons are radiated randomly in all directions In a laser, an atom undergoes a transition and emits a photon in the presence of many other photons that have energies equal to the atom s transition energy A process known as stimulated emission causes the light emitted by this atom to propagate in the same direction and with the same phase as surrounding light waves Section 29.7

32 Helium-Neon Laser (a) Emission and absorption processes (b) Decay of excited atoms (c) Stimulated emission of photons from a population inverted mixture of atoms in the excited and ground state

33 Lasers, cont. Laser is an acronym for light amplification by stimulated emission of radiation The light from a laser is thus a coherent source Mirrors are located at the ends of the bulb (laser tube) One of the mirrors lets a small amount of the light pass through and leave the laser Section 29.7

34 Lasers, final Laser can be made with a variety of different atoms One design uses a mixture of Ne and He gas and is called a helium-neon laser The photons emitted by the He-Ne laser have a wavelength of about 633 nm Another common type of laser is based on light produced by light-emitting diodes (LEDs) These photons have a wavelength around 650 nm These are used in optical barcode scanners Section 29.7

35 Force Between Atoms Consider two hypothetical atoms and assume they are bound together to form a molecule The binding energy of a molecule is the energy required to break the chemical bond between the two atoms A typical bond energy is 10 ev Section 29.7

36 Force Between Atoms, cont. Assume the atom is pulled apart by separating the atoms a distance Δx The magnitude of the force between the atoms is F A Δx of 1 nm should be enough to break the chemical bond This gives a force of ~1.6 x 10-9 N PE x PE x 10eV 1nm 19 9 F ( J / ev ) N Section 29.7