1. Chemistry is in the electrons To understand the periodic table and chemistry, we must understand the electronic structure of the atom – how the electrons are arranged

2. Learning objectives Describe the properties of waves Describe the photon and the relationship between light frequency and energy Describe the basic principles of the Bohr model Distinguish between the “classical” view and the “quantum” view of matter

3. Rutherford’s epic experiment revealed the positive nucleus with the electrons occupying the vast void around it Why don’t the electrons collapse into the nucleus?

4. The planetary idea A planet in a stable orbit will circulate indefinitely Unlike a moon, an orbiting charged particle will spiral inwards to the nucleus emitting energy as it does so

5. “Conventional” explanations do not work Yet we know that atoms exist and that electrons are stable outside the nucleus. Another explanation must be found

6. Let there be light Electromagnetic waves are characterized by a wavelength, a frequency, and an amplitude. (a) Wavelength is the distance between two successive wave peaks, and frequency is the number of wave peaks that pass a fixed point per unit time. Amplitude is the height of the maximum measured from the center line. different colours of electromagnetic radiation are waves with different wavelengths and frequencies.

7. Wavelength and frequency are related All electromagnetic radiation has the same velocity: the speed of light (c) = 3 x 10 8 m/s Velocity (c/ms -1 ) = wavelength (λ/m) x frequency (ν/s -1 ) Wavelength proportional to 1/frequency - as λ ↑ ν ↓

8. The electromagnetic spectrum consists of a continuous range of wavelengths and frequencies, from radio waves at the low- frequency end to gamma rays at the high-frequency end. The familiar visible region accounts for only a small portion near the middle of the spectrum. Note that waves in the X-ray region have a length that is approximately the same as the diameter of an atom (10 –10 m). Harmful radiation

9. Atoms emit and absorb radiation at specific wavelengths Absorption is light removed by the atom from incident light Emission is light given out by an energetically excited atom The absorption and emission lines are at the same wavelengths The lines from the H atom form a neat series. Do these spectra have anything to do with the electronic structure?

10. Each element has a unique spectrum Electronic structures of each element are different Spectra can be used to identify elements – even in very remote locations

11. Empirical classification of the spectra of the hydrogen atom All of the lines in the H atom spectrum can be fit to an equation The Balmer–Rydberg equation. –m and n are integers (n > m) –R is the Rydberg constant The wavelength of the transition from the lower level m to the upper level n

12. So, everything is cool with waves? Observations of radiation from heated bodies could not be described using classical methods Shortcomings with waves and the particle- like nature of radiation…

13. Blackbody radiation and Planck’s explanation Observations of radiation from heated bodies could not be described using classical methods Observed radiation exhibits a maximum that depends on the temperature of the body –As T ↑, λ max ↓

14. Quantization and the Planck equation The observed blackbody radiation phenomenon was susceptible to explanation if it was assumed that energy is emitted in discrete amounts instead of changing continuously E = hν h is Planck’s constant = 6.626 x 10 -34 Js

15. The bottom line As frequency increases, photon energy increases “Dangerous” radiation has high photon energy – UV light, X-rays Harmless radiation has low photon energy – IR, radiowaves

16. Light is a particle – the photoelectric effect Light incident on a metal surface causes electrons to be emitted. Below threshold frequency nothing happens Above threshold, current increases with intensity No current flows Current flows

17. Quantization of energy Light energy is “quantized” into units or packets Each packet is called a photon Photon size depends on the frequency E = hν As frequency increases so does the photon energy

18. Light: particle or wave or both? Newton advanced a corpuscular theory of light, even as he discovered the diffraction of light in a prism Huygens developed a wave theory of light Discovery of light interference and its description by wave theory made the latter triumphant in the 19 th century

19. Bohr’s theory of the atom – first attempt at explaining the structure Electrons are allowed to occupy certain levels (orbits) and no others Electrons can switch levels by absorbing or emitting energy (photons) exactly equal to the gap between the levels

20. Size of energy gap determines photon energy Small energy gap, low frequency, long wavelength (red shift) High energy gap, high frequency, short wavelength (blue shift)

21. The full spectrum of lines for H Each set of lines in the H spectrum comes from transitions from all the higher levels to a particular level. The lines in the visible are transitions to the second level

22. Shortcomings of Bohr Could not explain why these levels were allowed Only successful agreement with experiment was with the H atom Introduced connection between spectra and electron structure Concept of allowed orbits is developed further with new knowledge Nonetheless, an important contribution, worthy of the Nobel prize

23. The missing link: electrons are waves too! Key to unlocking the low door to the secret garden of the atom lay in accepting the wave properties of electrons Very small things behave differently from large ones De Broglie wave-particle duality All particles have a wavelength – or wavelike nature. This is significant only for very small particles – like electrons or photons (no mass). As mass increases, wavelength decreases. Electrons have wavelengths about the size of an atom. This makes electrons useful in studying matter – electron microscopy

24. De Broglie relation E = mc 2  m = E/c 2 But, E = hc/λ, so m = h/cλ λ = h/mv –For the electron, m = 9 x 10 -31 kg and v = 2 x 10 6 ms -1 –λ = 3 x 10 -10 m The electron’s wavelength is of the order of the atomic diameter

25. Wavelengths of large objects Should we be concerned about the wave- particle nature of large objects? Consider a baseball pitched at 100 mph. –m = 120 g and v = 45 m/s –λ = 10 -34 m For normal size objects, the wavelength will be immeasurably and irrelevantly small

26. Standing waves and strings Strings of fixed length can only support certain wavelengths. These are standing waves.

27. The Bohr orbits revisited The allowed orbits have a circumference equal to a fixed number of wavelengths All others disappear via destructive interference Orbit has exact number of wavelengths OK Orbit has inexact number of wavelengths BAD

28. Heisenberg Uncertainty Principle: getting to grips with the electron We can exactly predict the motion of a ball; But not an electron

29. Heisenberg Uncertainty Principle The position and momentum of a particle cannot be measured simultaneously to unlimited accuracy Δx Δp > 0

30. Explaining the uncertainty principle The act of “seeing” an electron using photons would transfer energy, causing a change in the electron’s energy, thereby changing its position As the object increases in size, the impact of the photon decreases There is a limit to the precision with which we can measure position and momentum

31. Heisenberg Uncertainty Relation In mathematical terms, Δx Δmv ≥ h/4π If the position is known precisely, Δx is small and the uncertainty in momentum is large If the velocity is known precisely, there is a high uncertainty in the position The electron will appear as a blur rather than a sharp point

32. Implications for the electron m = 9 x 10 -31 kg, v = 2 x 10 6 m/s If uncertainty in v is 10%, –Δmv = 2 x 10 5 x 9 x 10 -31 kgm/s –Δx ≥ h/4π18 x 10 -26 m – ≥ 6 x 10 -34 /4π18 x 10 -26 m – ≥ 3 x 10 -10 m or 300 pm Diameter of the H atom is about 100 pm

33. Quantum effects: when should we care? The Correspondence Principle states that quantum effects disappear when Planck’s constant is small compared to other physical quantities