Unit 3-1 wave-particle duality of electron and light

1. Unit 3-1 wave-particle duality of electron and light Chap 7

2. The Dilemma of the Atom • Electrons outside the nucleus are attracted to the protons in the nucleus • Charged particles moving in curved paths lose energy • What keeps the atom from collapsing?

3. Answering the Dilemma of the Atom • Treat electrons as both waves and particles, called wave-particle duality • Like light.

4. Matter and energy • Our world is made of two things: • Matter : whichever has mass. • Energy : • Electricity • Heat • Waves: light, sound

5. Waves • the distance between corresponding points on adjacent waves is the wavelength (), in unit of meter • The number of waves passing a given point per unit of time is the frequency (), in unit of s-1. • The time needed to pass a wavelength is the period (T),in unit of second. • T= 1/  • For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.

6. Electromagnetic radiation propagates through space as a wave moving at the speed of light. c =  c = speed of light, a constant (3.00 x 108 m/s)  = frequency, in units of hertz (hz, sec-1)  = wavelength, in meters

7. Diffraction – a special wave feature • when traveling waves encounter an obstacle or opening in a barrier that is about the same size as the wavelength, they bend around it – this is called diffraction • traveling particles do not diffract Tro, Chemistry: A Molecular Approach

8. Diffraction • the diffraction of light through two slits separated by a distance comparable to the wavelength results in an interference pattern of the diffracted waves • an interference pattern is a characteristic of all light waves

9. however, electrons actually present an interference pattern, demonstrating the behave like waves Electron Diffraction Tro, Chemistry: A Molecular Approach

10. Electromagnetic Radiations (light) • All electromagnetic radiation travels at the same velocity: the speed of light (c), 3.00  108 m/s. • Therefore, c = /T= • Remember the sequence and visible light wavelength!

11. The particle nature of light • The wave nature of light does not explain how an object can glow when its temperature increases. • Max Planck explained it by assuming that energy comes in packets called quanta, which is carried by photon.

12. Photon a particle of light. Electromagnetic radiation ALL light. Visible AND invisible visible light , x-rays, gamma rays, radio waves, microwaves, ultraviolet rays, infrared.

13. The energy (E ) carried by each photon of electromagnetic radiation is directly proportional to the frequency () of the radiation. E = h E= Energy, in units of Joules (kg·m2/s2) h= Planck’s constant (6.626 x 10-34 J·s) = frequency, in units of hertz (hz) or sec-1

14. The Nature of light • Therefore, if one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light: c =  E = h

15. Wavelength Table Long Wavelength = Low Frequency = Low ENERGY Short Wavelength = High Frequency = High ENERGY

16. Homework • Page 314, question 39, 41 a and b, 43

17. Bohr Model of H Atom and emission spectra

18. Hg He H Exciting Gas Atoms to Emit Light with Electrical Energy Tro, Chemistry: A Molecular Approach

19. Emission Spectra Tro, Chemistry: A Molecular Approach

20. The emission spectra • When light goes through a certain chemical gas: • One does not observe a continuous spectrum, as one gets from a white light source. • Only a line spectrum of discrete wavelengths is observed.

21. Bohr Model of H Atoms • Electrons orbit about nucleus on energy level /shell (n). • Each energy level has a defined distance to nucleus. • Electrons can jump from one level or another if receiving or releasing energy.

22. Bohr’s model of H atom • The energy of one electron on the shell n, En can be calculated by the following formula: • En = • 2.178  10−18 J= RH,called Rydberg constant.

23. Bohr’s model of H atom The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: Ef -Ei =E = −2.178x10-18 ni and nf are the initial and final energy levels of the electron.

24. 1 nf2 ( ) - = −RH 1 ni2 Predicting emission spectrum of Hydrogen • the wavelengths of lines in the emission spectrum of hydrogen can be predicted by calculating the difference in energy between any two states • for an electron in energy state n, there are (n – 1) energy states it can transition to, therefore (n – 1) lines it can generate • the Bohr Model can predict these lines very accurately

25. Hydrogen Energy Transitions

26. ni, nf DEatom Ephoton l Example 7.7- Calculate the wavelength of light emitted when the hydrogen electron transitions from n = 6 to n = 5 Given: Find: ni = 6, nf = 5 l, m Concept Plan: Relationships: E=hc/l, En = -2.18 x 10-18 J (1/n2) DEatom = -Ephoton Solve: Ephoton = -(-2.6644 x 10-20 J) = 2.6644 x 10-20 J Check: the unit is correct, the wavelength is in the infrared, which is appropriate because less energy than 4→2 (in the visible)

27. Practice – Calculate the wavelength of light emitted when the hydrogen electron transitions from n = 2 to n = 1

28. ni, nf DEatom Ephoton l Calculate the wavelength of light emitted when the hydrogen electron transitions from n = 2 to n = 1 Given: Find: ni = 2, nf = 1 l, m Concept Plan: Relationships: E=hc/l, En = -2.18 x 10-18 J (1/n2) DEatom = -Ephoton Solve: Ephoton = -(-1.64 x 10-18 J) = 1.64 x 10-18 J Check: the unit is correct, the wavelength is in the UV, which is appropriate because more energy than 3→2 (in the visible)

29. Bohr model and quantum mechanical model • Bohr model failed to predict other elements’ emission spectrum. Why? • There is only one e- in H. Each shell / energy level (n) is degenerate (unified). • In multiple-electron atoms, there are subshells have hold different energy, in each shell. • His model is replaced by quantum mechanical model. • His model is only useful to predict the emission spectrum of H.

30. Homework • Page 315 64, 67 b and c.