Physics Teach Yourself Series Topic 15: Wavelike nature of matter (Unit 4)
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1 Pysics Teac Yourself Series Topic 15: Wavelie nature of atter (Unit 4) A: Level 14, 474 Flinders Street Melbourne VIC 3000 T: W: tss.co.au E: TSSM 2017 Page 1 of 8
2 Contents Wat you sould now... 3 As it appears in Unit De Broglie Wavelengt... 3 As it appears in Unit Review Questions... 4 Alternative forula for de Broglie Wavelengt... 5 As it appears in Unit Review Questions... 5 Diffraction... 6 As it appears in Unit Electron Diffraction Patterns... 6 As it appears in Unit Review Questions... 6 Potons and Atoic Structure... 6 As it appears in Unit Review Questions... 6 Bor s Energy Levels of Hydrogen & Standing Waves... 6 As it appears in Unit Review Questions... 6 Solutions to Review Questions... 6 TSSM 2017 Page 2 of 8
3 As it appears in Unit 4 Wat you sould now Calculate te de Broglie wavelengt of atter, p Copare te oentu of potons and of atter of te sae wavelengt including calculations using p Interpret electron diffraction patterns as evidence for te wave-lie nature of atter Copare te diffraction patterns produced by potons and electrons Explain te production of atoic absorption and eission spectra, including tose fro etalvapour laps; Interpret spectra and calculate te energy of potons absorbed or eitted, ΔE = f Analyse te absorption of potons by atos in ters of te particle-lie nature of atter te cange in energy levels of te ato due to electrons canging state te frequency and wavelengt of eitted potons, E = f= c Describe te quantised states of te ato in ters of electrons foring standing waves, recognisingtis as evidence of te dual nature of atter De Broglie Wavelengt As it appears in Unit 4 It as been found tat te oentu of particles (atter) is given by p v. De Broglie suggested tat te expression studied in te topic of potoelectric effect, wic was used f to obtain te oentu of a poton, also applied to atter, tat is p v c TSSM 2017 Page 3 of 8
4 By siply rearranging te equation, we can obtain te forula of te de Broglie Wavelengt or tewavelengt of a Matter Wave: p v Were = te de Broglie wavelengt of a particle () 34 = Planc s constant = (Js) p = te oentu of te particle (gs -1 ) = te ass of te particle (g) v = te velocity of te particle (s -1 ) Warning:te Electron-volt value of Planc s constant, tis forula evs, does not applywen using Please note tat atter waves are not noticeable every daybecause te wavelie properties of atter will be noticeable only if te size of te de Broglie wavelengt is coparable to te size of te relevant aperture and obstacle. Review Questions 1. Find te de Broglie wavelengt of te following objects. a. A car wit a ass of1000 g, travelling at speed of b. A 3 g cat waling at 2 s -1. c. Will te car or te cat diffract wen tey pass troug a fully open door (about 1 wide)? Can you notice te wave-lie properties of tese objects.wy or wy not? 2. Calculate te wavelengt of an electron travelling at a speed of s -1. TSSM 2017 Page 4 of 8
5 Alternative forula for de Broglie Wavelengt As it appears in Unit It as been found tatte Kinetic Energy of a particle is given by E v. Rearranging te forula, 2 2E 2E we obtain v. Substituting te derived v into p v. p 2E. Substituting te oentu expression into de Broglie s wavelengt forula, we ave te alternative forula for te de Broglie Wavelengt: 2E Were = te de Broglie wavelengt of a particle () 34 = Planc s constant = (J s) = te ass of te particle (g) E = te Kinetic Energy of te particle (J) Review Questions 3. A 400g tennis ball as inetic energy of 760 J. Wat is te de Broglie wavelengt of tis tennis ball? 4. Calculate te wavelengt of an electron tat as been accelerated fro rest troug a potential 31 difference of 100 V. Te ass of an electron is g. TSSM 2017 Page 5 of 8
6 Solutions to Review Questions 1. a s p v b p v 3 2 c. No, because teir de Broglie wavelengts are uc saller tan te gap. No, because teir de Broglie wavelengts are too sall p v E W Ue qv E E E ev J E TSSM 2017 Page 6 of 8
7 5. a. E poton f c c E poton b. It can be concluded tat te electrons ave te sae wavelengt and oentu as te X-rays. c. electron Xray d. 2E ( ) E ( ) 16 J E ev 6. E f E E ev poton n 7. E poton f c f Hz 8. Any two of te arrows sown in te diagra on te rigt. (Tere are oter possible absorptions to iger energy levels as well.) TSSM 2017 Page 7 of 8
8 9. a. E f E E ev poton n b. E f E E ev poton n 10. Tey pass troug te gas uncanged. 11. Potons, wit energy greater tan 13.6 ev, could supply sufficient energy to ionize te ydrogen atos. 12. a. n 5 n 4 (lowest poton energy) E poton f E E n ev b. E poton f c 15 8 c E poton 13. Transition of n 3 n 1 corresponds to sortest wavelengt (igest poton energy) of ligt eitted. E E poton poton f f E c E n ev 15 8 c E poton TSSM 2017 Page 8 of 8
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