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From Ideas to Implementation When electrons (cathode rays) accelerate they produce x-rays. Heater on anodes βboils of electronsβ β electrons leave surface more easily with added heat. Velocity Selector Crossed Magnetic and electric fields J.J. Thompson 1897 Crossed Field Apparatus Anode Cathode x x X x x x x x x πΉπππ = ππ£π΅ (π£ = πππππππ‘π¦) Therefore when no deflection in crossed magnetic and electric fields ππΈ = ππ£π΅ π£= πΈ π΅ = π ππ΅ 1 π = π’π‘ + ππ‘ 2 2 By measuring deflection of cathode rays using location of βs β can be found 1 ππΈ π 2 π¦= ( ) 2π π£ π¦= 1 ππ π 2 ( ) 2 ππ π£ π β« π½π½ πβπππ ππ 1897 β« π πβππππ πππ π πππ‘ππ πππ’ππ β ππππ π‘πππ‘ πππ πππ πππππ πππ‘βππ πππ‘ππ ππππππππ‘πππ β π‘βπππππππ πππ‘βπππ πππ¦π π€πππ ππππππ’πππ ππ’πππππππ‘ππ ππππ π‘ππ‘π’πππ‘π ππ πππ‘π‘ππ >> βPlum puddingβ atomic model Electrons Travelling in magnetic field Electrons travel in the arc of a circle (not parabolic) as mag force is always perpendicular to the motion of the electron. Fluorescent Paint Mass of electron Robert Millikon (1911?) Apparatus floated oil drops using electric force. Oil drops became charged when sprayed. Process: 1. Measure terminal velocity >> mass of oil drops 2. Connect plates to power supply β when drop hovers >> ππΈ = ππ where q = charge on oil drop and E = electric field strength πβπ£ = ππ π πππ π= βπ£ Was found: ο· It was found the charge for every oil drop the charge was a multiple of 1.6 × 10β19 C coulombs. ο· The smallest charge found was 1.6 × 10β19 C coulombs. Mass spectrometer Velocity Selector β Crossed magnetic field and electric fields. Voltage used so that πΉππ = πΉπππ . . . . . . . . . . . . . . . . . . . Ion beam .Ion beam in circular arc due to fmag π£2 π= π π π£2 = π π ππ£π΅ π£ 2 = π π ππ΅ π£ = π π π π = ππ΅ π£ ππ΅π π€βπππ π = πππππ’π ππ πππππ’πππ πππ‘β π£ π£ = π£ππππππ‘π¦ ππ πππ (π£ππππππ‘π¦ π πππππ‘ππ) π = πβππππ ππ πππ π= Photoelectric effect Discovered 1887 - The ejection of electrons from surface of metal due to EM radiation Cause Oscillation electric field of EM wave causes electron to move >> generates magnetic field which interacts with magnetic field of EM wave Facts πππ‘π ππ π β² π ππππ‘π‘ππ πππ π πππππ β πππβπ‘ πππ‘πππ ππ‘π¦ Stopping voltage = voltage just required to stop the emitted electrons. Generated current is called photocurrent. Loss of KE = increase in electric PE Electron volt 1ππ = ππππππ¦ πππ’ππππ ππ πππ π‘ ππ¦ πππππ‘πππ π€βππ πππ£ππ π‘βπππ’πβ πππ‘πππ‘πππ ππππ ππ 1π Photoelectric facts 1. πβππ‘πππ’πππππ‘ β ππππβπ‘πππ π ππ πππβπ‘ π(π) β πΌππ‘. (ππππ£ππππ π > π0 ) 2. KE of emitted electrons is independent of intensity 3. The KE of emitted electrons depends on frequency 4. There is no emission below a threshold (π0 ) regardless of intensity 5. π0 is different for each metal (itsβs lowest for alkali metals / for elements with lowest ionisation energy) 6. If electrons are emitted, the emission is instantaneous Einsteinβs explanation of photoelectric effect 1. The energy of an EM wave is not spread out over the wave front. It concentrates in bundles (quanta / photons) 2. The energy of a quantum is related to frequency of the EM wave πΈππ’πππ‘π’π = βπ β = ππππππ β² π πΆπππ π‘πππ‘ = 6.6 × 10β34 3. During photoemission the energy of a quatum is completely absorbed by an electron 4. In getting out of the metal some of the energy acquired by the electron is lost π€ = ππππππ¦ πππ π‘ ππ π€ππ¦ ππ’π‘ = πππππ ππ‘πππ ππππππ¦ (π€πππ ππ’πππ‘πππ) πΎπΈπππ₯ = βπ β π€ Black body Radiation Black body : ο· Perfect absorber ο· Best emitter when heater ο· Stars behave like black bodies ο· As temp increases >> red >> orage >> yellow >> white >> bluish Hertz 1887 Confirmed existence of EM waves Wavelength was found using interference properties. A metal plate was used to reflect waves β created 2 waves and interference patterns. e.g. when waves superimpose the sparks at the collector may be twice as big or zero In radios f is altered by the 2 electron delays β the size of coils and plates. Causes other fβs to be excluded as the current oscillates at a natural frequency. In normal circuits As the switch is closed Circuits with solenoids I I t t The separate coils act like moving magnets as current increases , as B increases the other coils oppose the movement of the βmagnetβ (due to lenses law) SEMI-CONDUCTORS Thermionic Devices Were used before semiconductors β switching was slow, devices were large, used lots of electricity, ran at high temperatures Diode One way conducting device β electrons flow from end as they can only escape from 1 side (due to heater) I t Triode Amplification devices β current applied to grid opposes the movement of electrons, the variations in the current are amplified by the electrons moving through. V ππππ πππππ Silicon- an intrinsic conductor ο· Is semi-conductor ο· Abundant element found in sand(silicon dioxide) ο· Hard to extract ο· Conductivity increases and then decreases as temperature increases - due to outer shell electrons locked up in covalent network bonds which become loose when heated Conduction in Semi-Conductors (Intrinsic conductors) 1. Movement of freed electrons (by heat etc.) 2. Movement of βholesβ (behaving as positively charge electrons β STEPWISE motion of loosely bound electrons from atom to the left by the freed electron) 3. Net current = freed electron + hole current = 2 x freed electron current 4. Doping Silicon is irradiated to improve conductivity 03 31 ππ14 + π10 β ππ14 0 π10 β π11 + πβ1 31 31 0 ππ14 β π15 + πβ1 N- type Semi-conductor Adding phosphorous to silicon makes N-type semiconductor as it gives donor electrons which are not bound in covalent bonds Consists of: 1. Dominant donor eβs 2. Freed eβs 3. holes P- type Semi-conductor Made by adding boron β leaves βholesβ (positive charge areas) Consists of: 1. Dominant donor hole current 2. Free electron current 3. Freed hole current + -- Forward biased reversed biased Semi-conductor diodes P-type stuck on to n-type The donor eβs and holes βwanderβ causing + and β charge to build up on the n and p side. When charge is applied to forward biased direction the depletion layer gets smaller >> increased conductivity When charge is applied to reversed biased direction the depletion layer gets bigger >> lousy conductor Therefore >> one way conductor + Semi-Conductor transistors First Invented by Bell telephone laboratories for telephone exchanges are Thermionic devices were no longer reliable/effective (late 1940s) AWA (Amalgamated Wireless Australia) - developed ways to use transistor 1. 2. 3. 4. 5. Voltage at base causes depletion layer to get smaller >> Electrons no longer repelled by negative area of depletion layer Current flows freely from emitter to collector Varying voltages at base allow varying levels of current through Transistor acts as amplifier Heavily doped (collector) β reversed biased Lightly doped (base) Heavily doped (emitter) Forward biased Computers and Chips Transistors are used as switches in computers 1. Big change in base voltage (on/off) 2. Collector is either on/off (1/0) 3. Acts as binary code device or Boolean gates Why are thermionic devices still used Vaccum triodes still used in guitar amps as sound reproduced is βWarmerβ β in Transistors it is more βedgyβ Making Silicon Chips 1. Silicon wafer prepared by melting, cutting polishing etc. 2. Thin layer of oxide added by heating in oven 3. Photoresist added to surface 4. Whole thing exposed to light through a mask 5. Area hit by light hardens 6. Other areas are etched away 7. Un covered areas Irradiated (doped) with atoms (Phos. Or Boron for n or p type) 8. New layer of silicon added 9. 3-7 repeated several times Up to 40 layers of silicon to make chips Impact of the invention of the transistor Impacts: ο· Allowed development of integrated circuits ο· Allowed development of advances electronics ο· computers + digital devices are used as sources of entertainment ο· Allowed development of computers ο· Improved telecommunications technology Advantages: ο· Allowed development of computers making lives easier ο· Improved quality of life ο· Improved telecommunication ο· Made life easier ο· Created many jobs in Information technology and electrical engineering ο· Increased wealth of information ο· Allowed storage of huge amounts of information ο· Increased rate of globalisation Disadvantages: ο· Manufacture and operation of integrated circuits requires vast amounts of energy >> enhanced greenhouse effect + climate change + pollution ο· Increasing human dependence on β« πππππ’ππ‘π technology for livelihood and enjoyment of life ο· Electronic waste >> pollution ο· Huge demand for resources e.g. sand, metal, coal ++++++ -------- Photocells 1. Photon hits p-n depletion layer/junction 2. Photon gets absorbed + creates an electron/hole pair -/+ 3. Electron/hole go in opposite direction due to charges of depletion layer +++++++++ ------------ Problems / design problems with photocells ο· Recombination β hole meeting electron by chance β loss of charge ο· Photon may not hit depletion layer Super conductors When certain conductors are below Critical temperature π < ππ resistivity goes to zero Can be cooled using liquid gases such as He and N2 1. Gas is compressed 2. Compressed gas is allowed to cool down 3. Gas expands as it is released 4. Gas particles do work 5. Gas particles lose KE 6. Gets cooler Cryogenics = science of low temperatures 1911 β scientists succeeded in near absolute zero temperatures (0 ° K) Type 1 superconductors If π΅ > π΅π impossible to turn metal into superconductor no matter how low temperature Metal Al Ga Hg In Nb Pb Sn π»π (π²) 1.176 1.083 4.153 3.408 9.26 7.193 3.722 π©π (π») 0.0105 0.0058 0.0411 0.0281 0.1991 0.0803 0.0305 Metal Tn Ti V W Zn π»π (π²) 4.47 0.39 5.3 0.015 0.85 π©π (π») 0.0829 0.010 0.1023 0.000115 0.0054 Type 2 superconductors (High temperature super conductors) Alloys of metals or ceramics (Complex Crystal structure) Very brittle >> hard to use X-Ray Diffraction β Braggβs experiment ο· ο· ο· ο· ο· ο· Uses property of all EM waves β Diffraction Designed by Bragg Diffraction effects increase as physical dimensions of aperture approaches the wavelength of the waves i.e. at the atomic scale Interference from diffraction The atomic distance can be determined by calculating the angles and the distances between the diffracted parallel rays ππ = ππ πππ π½ πππππ π = ππππππππππ ππ ππππ π = ππ πππππππ π, π, π β¦ π½ = π ππππππππππ πππππ ππ π ππππππ BCS theory of superconductivity 1. An electron passes between ion lattice, pulling ions slightly closer together >> causes increased concentration of + charge (if π > ππ random vibrations of lattice ions totally dominate this small effect) 2. Increased conc. of + charge attracts another electron (preventing it from colliding with lattice ions) so that the 2nd e moves into space between the ions 3. Effectively there is a pair of electrons (copper pair) moving in the space between the lattice ions, the first one disturbing the lattice which in turn keeps the 2nd e also moving in space between the ions >>>> fudge >>> however only theory that can make predictions that can be experimentally verified Max current in Super Conductor π΅ < π΅π πΎπΌ < π΅π π πΎπΌ < ππ΅πΆ πΌ< ππ΅π πΎ Current is confined to the surface of super conductors. >> No B in the interior >> non penetration of B into superconductor >> Meissner Effect Magnetic Levitation Due to Meissner effect >> induced eddy currents in super C gen. fields that repel the external mag field >> eddy currents continue until super conductor heats up From Quanta to Quarks Ernest Rutherford β 1871 β 1937 ο· New Zealand born physicist worked with Thomson 1856-1940 at Cavendish Lab Cambridge university ο· Brilliant Experimental physicist ο· His work with alpha particles Disproved JJ Thomsons plum pudding atomic model Rutherfordβs Gold foil experiment β designed by Rutherford conducted by Hans Geiger and Ernest MArsden 1. Fired alpha particles at very thin gold foil 2. Measured angles of diffraction 3. Majority of particles went straight through and some bounced back o Passing through β meant mostly empty space o Some bouncing back β βas incredible as if you had fired a 15 inch shell at a piece of tissue paper and it came back and hit youβ β means huge conc. of charge in a certain place 4. This contradicted the predictions of greater deflections of Thomson plum pudding model 5. Showed that atoms were mostly empty space with huge concentration of charge in nucleus 6. Were able to determine approx. size and charge of nucleus Deductions β 79 positive charge units (79 * 1.6 * 10^-19 coulombs) >> nuclei have charges that are integral multiples of e >>> most be particles in nucleus Rutherfordβs atomic model Carbon 12 β Nucleus = 12 protons + 6 electrons , 6 orbiting eβs Uranium 238 β Nucleus = 238 Pβs + 146 eβs , 92 orbiting eβs >>> was model explaining alpha and beta decay Rutherford unhappy due to idea of eβs in nucleus Found isotopes always differed by a P and E or more >>> Neutron???? 1919 First Artificial transmutation ο· Fired Alpha particles at enough H2 gas to completely stop all particles ο· However scintillations were observed ο· Were Proton scintillations ο· Alpha collisions caused protons to fly hit screen ο· Repeated with enough N2 gas to stop all particles ο· Proton scintillations observed ο· Conclusion >> protons were in other atoms Speculation whether π»π24 + π714 β π817 + π11 ππ π»π24 + π714 β πΆ613 + π»π24 + π»11 Not 2nd one as only 2 trails after collision in Wilson Cloud Chamber Experiment >> therefore alpha is absorbed in collisions. Discovery of Neutron Adding more paraffin increased counts on Geiger counter >> in fact adding anything with lots of H+ did Chadwick analysed the results of this experiment and concluded that the radiation was possible neutrons. By analysing the speeds of the particles he was able to find the approximate mass of the neutron. Nuclear force ο· The positive electrons exert a huge electrical repulsion force on each other (approx. 25.6N between opp. Protons at edge Au atom) ο· However nucleus is stable ο· Must be a force holding the nucleus together ο· This forced called βNuclearβ force β it is short range Binding Energy = energy needed to pull atom apart = energy released when atom is made from its components Energy Released 1. = (π‘ππ‘ππ πππ π ππ πππππ‘πππ‘π β π‘ππ‘ππ πππ π ππ πππππ’ππ‘π ) ππ πππππππππ × π 2 πππ π πππ π‘ ππ ππππππ¦ 2. = π‘ππ‘ππ π΅πΈ πππππ’ππ‘π β π‘ππ‘ππ π΅πΈ πππππ‘πππ‘π π. π. = Nuclear forces In large atoms 1. Close Nucleons attracted to each other by strong nuclear force 2. However distant nucleons have less of this (e.g. ones on opposite sides of large nucleus) due to short range of nuclear force 3. Tug of war ( local strong nuclear attracting forces VS. weaker electric repulsion ) IF a heavy nucleus is split into 2 smaller nuclei, energy would be released β as smaller nuclei have greater BE/nucleon Nuclear reactions 144 235 239 40 π10 + π92 β π92 β ππ38 + ππ54 + 2π10 ππ 92 1 β πΎπ36 + π΅π141 56 + 3π0 Fission products ο· ο· ο· The released neutrons go to cause other U-235 Fission causing reaction to be self-sustaining >> lots uncontrolled fission reaction The Fission of U-238 does not produce stray neutrons >> cannot not sustain reaction >> not as useful in reactors or bombs. 238 239 0 239 However U-238 can be used to make Ploutonium-239 π10 + π92 β ππ93 + πβ1 β ππ’94 which fissions to produce neutrons Discoveries about Nuclear fission 1. Enrico Fermi (1901-1954) led the world in neutron physics. a. Bombarded as many elements as possible with neutrons b. When done with uranium >>> resulted in delayed emiision of beta particle >>> resulted in production of element with high atomic number >>> first transuranic element made (transuranic element = element with atomic number > 92) 2. Slow Neutrons are more effect that fast neutrons a. Fermiβs co-workers (Edoardo Amaldi 1908-1989 and Bruno Pontecorvo 1913-1993) found experiment had different results in diff. parts of room e.g. on wood table or marble β best results with wooden talbe b. Fermi investigate phenomenon. He put paraffin in front of neutron source >>> result massive increased in intensity of reactions c. Conclusion >> Slow Neutrons are better at causing fissions d. This is because slow neutrons are unrepelled by the nucleus and spend greater time in vicinity of nucleus >> more chance of being captured 3. Lise Meitner and Frisch Strassman Identify Fission a. Meitner and Frisch received letter from Otto Hahn who Studied transuranics from neutron bombardment of heavy elements >>> found barium >>> didnβt know where it came from b. The calculated that if uranium nucleus were split the two parts would be forced apart at energiesβ of about 200 Mev c. Meitner calculated that if the uranium nucleus were split then the mass defect of the products was 200Mev d. Calculations confirmed fission of uranium >> explained origin of barium 4. The First observations of fission a. Frisch returned to Copenhagen. Bombarded uranium with neutrons, emitted particles passed into cloud chamber b. 2 Short Fat cloud trails were observed c. Confirmed fission reaction Manhattan project 1. Leo Szilard idea of chain reaction sparked researched in nuclear weapons. He was sure that it was possible. 2. Approached Einstein in 1939 and urged him to write letter to President Roosevelt suggesting USA should actively research the possibility of a nuclear bomb. 3. In 1942 US gov. made agreement to work with British government on designing and constructing nukes >> MANHATTAN PROJECT 4. Was though there were 2 pathways to A-Bomb. Using Uranium-235 or Plutonium 239 as fuel. Unsure which would be better the US Gov. decided to proceed with both methods a. Uranium enrichment i. U-234 0.006% , U-235 0.7%, U-238 99.3% ii. Gaseous diffusion π β ππ2 β ππΉ6 (π) Gas Repeatedly passed through membrane filters, the lighter + faster moving U-235 hexafluoride passes through it is a wasteful process iii. Centrifuge technique ππΉ6 (π) is spun in a centrifuge, the heavier U-238 is pushed to the sides 238 239 0 239 b. Creating Plutonium π10 + π92 β ππ93 + πβ1 β ππ’94 5. Developed nuclear reactors to produce plutonium for nukes - they are now mostly used for power generation a. Control rod (neutron absorbers) used to absorb neutrons and control reaction b. Moderator slows neutrons to increased likelihood of fission with U-235 i. Usually small nuclei elements β neutrons that collide with small nuclei pass on some momentum and slow down (whereas a large nucleus would reflect) ii. Originally used graphite β as readily available, obtained and pure HOWEVER can catch on fire (Chernobyl) iii. Heavy water (where the hydrogen is deuterium) or water (Last resort) c. Heat from coolant is piped to heat exchanger or directly to turbine to turn generator Fast Reactors ο· ο· ο· ο· Plutonium Fuel 20% No moderator as plutonium fission best with fast neutrons Can be made to make plutonium than it uses β U238 lines core More risk for nuclear explosion due to lots of plutonium Nuclear explosions from reactors ο· Impossible due to lack of critical mass ο· Can melt down (literally) if reaction is too fast + uncontrolled Nuclear waste ο· Can be reprocessed β chemical extraction of useful isotopes from spent fuel rods o Not popular as dangerous and possible to make nukes ο· OR Storage deep underground in geographically stable places Spectral lines of hydrogen β Balmerβs Equation Was found that 1 π = π β ( 1 22 β 1 π2 ) by analysis of spectral lines of hydrogen π (ππ’ππππ ππ π ππππ‘πππ ππππ) = 3,4,5,6 β¦ πππ π β (π π¦πππππβ² π πΆπππ π‘πππ‘) = 1.0096 × 107 π = π€ππ£ππππππ‘β ππ π ππππ‘πππ ππππ 1 1 π π2 Furthermore = π β ( 1 π2 β΄ β ) π€βπππ π > π and are integers π 1 1 = π β ( 2 β 2 ) π π π π = ππ β ( 1 1 β 2) 2 π π 1 1 πΈπβππ‘ππ = βπ = βππ β ( 2 β 2 ) π π = (β π€βπππ β = πππππππ ππππ π‘πππ‘ βππ β βππ β ) β (β ) π2 π2 = πΈπ β πΈπ π β πππππ πππ πππππ βπππ πππππ‘, π β πππππ πππ π π‘πππ‘πππ πππππ‘ β΄ πΈπππππ¦ ππ πππππ‘πππ ππ π π» π΄π‘ππ ππ ππ’πππ‘ππ ππ πππππ ππ‘πππ ππππππ¦ πππ βπ¦ππππππ = πππππππ ππππππ¦ πππ π» ππ‘ππ = βππ = 13.6eV βπ = (β 1 22 = βππ ( βππ β β 42 1 ) 42 ) β (β βππ β 22 where electron jumps from 4th to 2nd orbit β΄ ο· ο· ο· Energy of electron is quantised Orbital radius is quantised Orbital speed is quantised Spectra series of hydrogen Lyman Series: m (lowest electron orbit in the series / normal e position) = 1 n =2,3,4β¦β Balmer series: m = 2 n =3,4,5β¦β Paschen series: m = 3 n =4,5,6β¦β Brackett series: m = 4 n =5,6β¦β Pfun series: m = 5 n =6,7,8,9β¦β Classical perspective Kinetic Energy of an electron Centripetal force for an electron in orbit is electrostatic attraction between nucleus protons and the electron β΄ πΉπππ = πΉππ πππ = 2 π ππ 2 = 2 π πΉ π= π π£ 2 ππ 2 = 2 π π π ππ 2 1 ππ£ 2 = π 2 1 ππ 2 ππ£ 2 = 2 2π Total energy of electron πππ ππ 2 πΈππππ‘πππππ ππΈ = β = β π π πΊππ ) π 2 2 ππ ππ ππ 2 β΄ π‘ππ‘ππ ππππππ¦ ππ πππππ‘πππ = β + = β π 2π 2π ππ 2 π‘ππ‘ππ ππππππ¦ = β 2π βπΆπ ππ 2 π€ = πππππππ ππππππ¦ = 2 = π 2π (ππ¦ πππππππ¦ ππ ππππ£ππ‘ππ‘πππππ ππΈ = β π= ππ 2 2π 2π π=β π Orbit period 2ππ (πππππ‘ π‘πππ) π= π£ 3 1 π£ 2 π€2 π= = =β π 2ππ m . πππ 2 ) Bohrβs Model of the atom Bohr awarded Nobel prize for physics in 1922 Bohrβs Postulates 1. Electrons in an atom exist in βstationary statesβ in which they possess unexplainable stability. Any permanent change in their motion must consist of a complete transition from one stationary state to another 2. In contradiction to classical ERM theory, no radiation is emitted from an atom in a stationary state. A transition between 2 stationary states will be accompanied by emission or absorption of EM radiation (a photon). The frequency of the photon is given by: βπ = πΈ1 β πΈ2 π€βπππ πΈ1 = ππππππ¦ ππ ππππ‘ππ π π‘ππ‘π πΈ2 = πππππ π π‘ππ‘π Bohrβs explanation of apparent classical nature of electron orbits Bohn said the Bumpiness (quantised nature) is not noticed in the shorter wavelengths (high transitional fβs) because the electron orbits are very close together. βππβ π‘ππππ ππ‘πππππ π (π΅πβπ) 1 1 π = ππ ( β 2 ) πππ π‘ππππ ππ‘ππππ πππ‘π€πππ ππππππππ‘ πππππ‘π 2 (π β 1) π = ππ ( 2π β 1 ) (π β 1)2 π2 β ππ ( π= 2π ) ππ π β β = π 2 π2 2ππ ππ π β β π3 πΈππ’ππ‘πππ ππππ π ππππ π πππ βππβ π‘ππππ ππ π‘πππππ π (ππβπ) 3 3 2cR 2 β = n3 m π€2 . πππ2 πππ 2 2 ( π2 ) β = . m πππ2 2 πππ π’ππ‘ π€βππ π ππ’ππππππ πππ‘β π ππππ β«> π = Quantisation of orbits ππ 2 ππ 2 π2 βππ (ππππ π ππππ) = π= . π ππππ π(πππππ ππ‘πππ ππππππ¦ πΆπΉ π€πππ ππ’πππ‘πππ) = 2 2π 2 βππ π ππ 2 β΄ π = π2 [ ] (π = 1,2,3,4 β¦ . . ) 2π»ππ β«> πππππ ππ πππππ‘πππ πππππ‘π ππ ππ’πππ‘ππ ππ ππ = 2 4 2π ππ π π2 β2 4π 2 ππ πππ2 Quantisation of angular momentum 2π 2 βππ (ππππ π ππππ) = β . 2 (πππ‘ππππππ‘πππ ππ’πππ‘π’π π‘βππππ¦) π=β π π π β3 π 2 βπ 2π 2 ππ 2 π 4 2π 2 ππ 2 π 4 = β . 2. π ππππ π = π π β3 π β3 π π£= 2πππ 2 1 . β π 2πππ 2 1 β2 π×π£×π = π. . . 2 . π2 β π 4π πππ 2 β΄ ππ£π = π. β β«β« ππππ’πππ ππππππ‘π’π ππ ππππ πππ£ππ 2π Limitations of Bohrβs atomic model ο· Only works for hydrogen (impossible to calculate the wavelengths of spectral lines of all other atoms) ο· Works well for atoms with one electron in outer shell but not when there are more ο· Bohr model does not explain why some electron transitions why some electron transitions are favoured (i.e. canβt explain why spectral lines are brighter) ο· Careful observations with better instruments showed other lines (known as hyperfine lines) β there must be some splitting of energy levels that Bohr model canβt explain ο· When gas is excited in magnetic field emission spectral lines are split (called Zeeman effect) β Bohr model cannot account for this ο· Bohr model is a mixture of classical and quantum physics β this is a problem. i.e. semi-classical >> not a true quantum theory Momentum of photons ο· Compton (US scientists) fired EM at electron clouds in 1923. ο· Found most electrons absorbed the EM gained energy and flew off ο· However at X-rays and above after collision the electron flies off and other photons are emitted at lower frequencies βπ π β π ο· Thought that ππ 2 = π. π = ο· ο· ο· Measured the energies of the scattered waves to test this idea Found to be true Conclusion >> photons with big p act more like particles β΄ ππβππ‘ππ = Louis De Broglie 1924 ο· Suggested that particles have wave properties ο· Said ββ¦if something that we normally think of having wave properties can, under some circumstances be thought of having particle propertiesβ (e.g. em wavres >> photons)β then perhaps things that we normally think of being particles can under some circumstances have wave characteristicsβ (electrons >> as waves) ο· His achievement was that he developed this idea mathematically ο· Suggested that the quantised nature and the stability seen in the Bohr Model was due to the βmatter wavelengthβ of the electrons and the relationships ππ = 2ππ and π = β ππ£ De Broglie βstanding waveβ pattern where Ξ» = wavelength of electron and m = electron mass and n = integer Evidence of De Broglie theory β Davisson and Germer Experiement 1927 ο· Fired electrons at rotating Nickel Crystals ο· Expected to go in random directions ο· HOWEVER the direction of the scattered electrons coincided with the predictions of Braggβs law which is usually applied to X-Rays ο· ο· ο· ο· ο· ο· Furthermore they calculated the wavelength to be one feined by De broglieβs formula G.P. Thomson (JJβs son) tried with gold foils β found interference patterns and diffraction CONCLUSION >> electrons have a wave properties PROBLEM >> WTF IS AN ELECTRON? SO what >> used whatever theories (wave or matter) to solve problems >>> Troubled Einstein