Understanding Light and Electrons: Waves and Particles

1. Ch. 4 - Electrons in Atoms I. Waves & Particles

2. Light and Electrons • Because light and electrons have common properties, understanding one helps to understand the other.

3. Electromagnetic radiation • Energy that exhibits wave-like behavior as it travels • Includes: gamma rays, X-rays, infrared, visible spectrum, microwaves, ultraviolet rays, radio and TV waves

4. EM Spectrum HIGH ENERGY LOW ENERGY

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

6. Waves • Wavelength () - length of one complete wave (measured in m, cm, nm) • Frequency () - # of waves that pass a point during a certain time period • hertz (Hz) = 1/s (s-1) • Amplitude (A) - distance from the origin to the trough or crest

7.  crest A A origin trough  Waves greater amplitude (intensity) greater frequency (color)

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

9. WORK:  = c   = 3.00  108 m/s 7.50  1012 Hz EM Spectrum • EX: Calculate the wavelength of radiation whose frequency is 7.50 x !012 Hz. GIVEN: • = 7.50 x !012 Hz  = ? c = 3.00  108 m/s = 4.00  10-5 m

10. Light as Particles • A property which could not be explained in terms of waves was a phenomenon known as the photoelectric effect – refers to the emission of electrons from a metal when heated or lit.

11. Quantum Theory • Planck (1900) • Observed - emission of light from hot objects • Concluded - energy is emitted in small, specific amounts (quanta) • Quantum - minimum amount of energy change

12. Classical Theory Quantum Theory Quantum Theory • Planck (1900) vs.

13. Quantum Theory • The energy of a photon is proportional to its frequency. E: energy (J, joules) h: Planck’s constant (6.6262  10-34 J·s) : frequency (Hz) E = h

14. Quantum Theory • EX: Find the energy of a photon with a frequency of 3.55  1017 Hz. GIVEN: E = ?  = 3.55  1017 Hz h =6.6262  10-34 J·s WORK: E = h E = (6.6262  10-34 J·s) (3.55  1017 Hz) E = 2.35  10-16 J

15. Quantum Theory • Einstein (1905) • Observed - photoelectric effect

16. Quantum Theory • Einstein (1905) • Concluded - light has properties of both waves and particles “wave-particle duality” • Photon - particle of light, having zero mass, carrying a quantum of energy

17. Quantum Theory • Radiation is emitted and absorbed only in whole numbers of photons

18. Ch. 4 - Electrons in Atoms II. Bohr Model of the Atom

19. A. Line-Emission Spectrum excited state ENERGY IN PHOTON OUT ground state

20. B. Bohr Model • Linked the atom’s electron with photon emission • e- exist only in paths, or orbits, with specific amounts of energy called energy levels • Therefore… • e- can only gain or lose certain amounts of energy • only certain photons are produced

21. Energy of photon depends on the difference in energy levels e- jumps up when energy is absorbed-gives off light when is falls back down B. Bohr Model 6 5 4 3 2 1

22. C. Other Elements • Each element has a unique bright-line emission spectrum. • “Atomic Fingerprint” Helium • Bohr’s calculations only worked for hydrogen! 

23. Bohr’s model of the atom explained electrons as particles.

24. A. Electrons as Waves • Louis de Broglie (1924) • Applied wave-particle theory to e- • e- exhibit wave properties

25. B. Quantum Mechanics • Heisenberg Uncertainty Principle • Impossible to know both the velocity and position of an electron at the same time

26. B. Quantum Mechanics • SchrödingerWave Equation (1926) • treated e- moving around the nucleus as waves • defines probability of finding an e- • defines mathematically the wave properties of electrons

27. Radial Distribution Curve Orbital B. Quantum Mechanics • Orbital (“electron cloud”) • Region in space where there is 90% probability of finding an e-