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Understanding Electrons: The Wave-Particle Duality in Modern Atomic Theory

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khalil
27 diapositives · 420 Views · Jul 23, 2014

This document explores the evolution of atomic theory, focusing on the dual nature of electrons as both particles and waves. Initially, Rutherford's model described atoms as having a dense nucleus with surrounding electrons, yet failed to explain their behavior. Advances in light absorption and emission studies led to the development of a new atomic model, highlighting the relationship between light and electrons. The text further discusses the electromagnetic spectrum, emphasizing spectroscopy, wave properties, and the quantum nature of light as understood through historical experiments by Max Planck and Albert Einstein.

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  1. Electrons in Atoms I. Waves and Particles

  2. A. A New Atomic Model • Rutherford model of the atom • Dense positively charged nucleus • Mostly empty space • Did not explain where the electrons are located around the nucleus • Did not explain why negative electrons did not move to the p+ in the nucleus and collapse atoms

  3. A. A New Atomic Model • Prior to 1900 : • Electrons are particles (concentration of energy and other properties in space and time) • Light is waves (energy spread out over a larger region of space and time; an oscillation that moves outward from a source.

  4. A. A New Atomic Model • New atomic model emerged as a result of experimentation with absorption and emission of light by matter. • Studies revealed a relationship between light and an atom’s electrons. • Light was shown to exhibit both particle and wave-like behaviors. • Electrons were also shown to exhibit dual wave-particle nature.

  5. B. Waves • Velocity (c) – Unit: m/s • Amplitude (A) - distance from the origin to the trough or crest. Unit will be length (m, …) • Wavelength () - length of one complete wave ; peak-to-peak distance. Unit: m, nm… • Frequency ( or f ) - # of waves that pass a point during a certain time period • hertz (Hz) = 1/s or s-1

  6. crest A A origin trough  B. Waves greater amplitude (intensity)

  7. B. Waves • Frequency & wavelength are inversely proportional c =  c: speed of light (3.00  108 m/s) : wavelength (m, nm, etc.) : frequency (Hz)

  8. WORK:  = c   = 3.00  108 m/s 2.73 x 1016 s-1 B. Waves • EX: Light near the middle of the ultraviolet region of the EM spectrum as a frequency of 2.73 x 1016 s-1. Calculate its wavelength. GIVEN:  = 2.73 x 1016 s-1  = ? c = 3.00  108 m/s = 1.10 x 10-8 m

  9. WORK:  = c   = 3.00  108 m/s 4.34  10-7 m B. Waves • EX: Find the frequency of light with a wavelength of 434 nm. GIVEN:  = ?  = 434 nm = 4.34  10-7 m c = 3.00  108 m/s = 6.91  1014 Hz

  10. C. Electromagnetic Spectrum • Electromagnetic radiation – a form of energy that exhibits wavelike behavior as it travels through space • Electromagnetic spectrum – all forms of electromagnetic radiation together

  11. R O Y G. B I V red orange yellow green blue indigo violet C. EM Spectrum HIGH ENERGY LOW ENERGY

  12. C. EM Spectrum HIGH ENERGY LOW ENERGY

  13. C. EM Spectrum • Spectroscopy – branch of science that studies the interaction of light and atoms. • Spectrum – pattern of  or  when electromagnetic radiation is separated into its parts. • Spectroscope – instrument used to measure the wavelength of light.

  14. C. EM Spectrum • Continuous spectra – use a diffraction grating to separate the wavelengths into the visible light spectrum. Shows all wavelengths in a given range. • Example : • visible light (400 nm – 700 nm)

  15. C. EM Spectrum • Emission (bright line) spectra • Each line = different wavelength of light. • Lines represent energy emitted as e- fall from excited state to lower/ground state (from high energy levels to lower energy levels) • Usage – analyze substances for elements present. Each emits its own color. (Stars/astronomy)

  16. C. EM Spectrum

  17. C. EM Spectrum • Absorption (black line) spectra – shows the fraction of incident radiation absorbed by the material over a range of frequencies.

  18. C. EM Spectrum • Ground state vs. excited state • Ground state – Electrons in the atom are in the lowest energy levels. • Excited state – Electrons in the atom are in higher energy levels. Electrons become “excited” when they gain enough energy to jump to a higher energy level in the atom. • Example: flames, spectral tubes

  19. D. Waves vs Particles • Waves can bend around small obstacles. • Waves can fan out from pinholes. • Particles effuse (trickle out) from pinholes. • Ex. Balloon gradually deflates.

  20. D. Waves vs Particles

  21. E. Particle Behavior of Light • Max Planck (1900) • Observed - emission of light from hot objects • Concluded - energy is emitted in small, specific amounts (quanta = bundle of energy)

  22. Classical Theory Quantum Theory E. Particle Behavior of Light • Planck (1900) vs.

  23. E. Particle Behavior of Light • Einstein (1905) – observed the photoelectric effect. Electromagnetic radiation strikes the surface of the metal, ejecting electrons from the metal, creating an electrical current.

  24. E. Particle Behavior of Light • Einstein (1905) • Concluded - light has properties of both waves and particles “wave-particle duality” • Light moves like a wave, but transfers energy like a stream of particles.

  25. E. Particle Behavior of Light • Photon – bundle of energy given off as light. A particle of electromagnetic radiation having zero mass and carrying a quantum of energy. • Quantum - minimum amount of energy that can be lost or gained by an atom

  26. E. Particle Behavior of Light • The energy of a quantum of energy is proportional to its frequency. E: energy (J, joules) h: Planck’s constant (6.6262  10-34 J·s) : frequency (Hz) E = h

  27. E. Particle Behavior of Light • EX: Find the energy of a red photon with a frequency of 4.57  1014 Hz. GIVEN: E = ?  = 4.57  1014 Hz h =6.6262  10-34 J·s WORK: E = h E = (6.6262  10-34 J·s) (4.57  1014 s-1) E = 3.03  10-19 J