Weird experiments Schrödinger equation

1. Weird experiments Schrödinger equation

2. Bohr model of an atom 1913 centrifugal is Latin for "center fleeing" It does not exist! http://regentsprep.org/Regents/physics/phys06/bcentrif/centrif.htm

3. Bohr model of an atom 1913 Potential energy of the electron “Introduction to wave phenomena” by Akira Hirose and Karl Lonngren

4. Bohr model of an atom 1913 Kinetic energy of the electron Total energy of the electron electron angular momentum

5. Bohr model of an atom 1913 electron angular momentum Niels Bohr postulated that the momentum was quantized h is Planck’s constant 6.626068 × 10-34 m2 kg / s The radius is found to be

6. Bohr model of an atom 1913 The energy then becomes quantized http://csep10.phys.utk.edu/astr162/lect/light/bohr.html

7. Photo electric effect - Einstein Energy of a photon E = h http://regentsprep.org/Regents/physics/phys05/catomodel/bohr.htmHoudon

8. Einstein’s explanation

9. Bohr model of an atom 1913 What is the frequency of the light that will be emitted by an electron as it moves from the n = 2 down to n = 1? Ionization implies n → 

10. Experiment to understand the photo electric effect.

11. Experimental conclusions • The frequency must be greater than a “cut off frequency” that changes with different metals. • Kinetic energy of the emitted electrons depends upon the frequency of the incident light. • Kinetic energy of the electrons is independent of the intensity of the incident light.

12. Sodium has a work function of W = 1.8 eV. Find the cutoff frequency. red

13. A metal with a work function of 2.3 eV is illuminated with ultraviolet radiation l = 3000 Ǻ. Calculate the energy of the photo electrons that are emitted from the surface.

14. Franck-Hertz experiment in mercury vapor. Electrons are accelerated and the current is monitored. 1914 (In 1887, Hertz noted that electrons would be emitted from a metal that was illuminated with light.) Current Voltage http://hyperphysics.phy-astr.gsu.edu/hbase/FrHz.html

15.  Reflected wave is strong if n = 2d sin d d sin

16. Davisson-Germer experiment – electrons incident on nickel 1925http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/davger2.html

17. Interpretation of the Davisson-Germer experiment Energy of a photon E = h Waves Particles

18. de Broglie wavelength de Broglie argued that there was a wavelength that could be written from

19. Interpretation of the Davisson-Germer experiment Conclusion Waves & particles have many similarities!

20. Schrödinger equation

21. Schrödinger equation

22. Schrödinger equation A wave can be written as Operator One dimension Three dimensions

23. Schrödinger equation What is the meaning?

24. 1 a0 -2 0 +2 Schrödinger equation a1 a0 a2 a1 a0 a2 a1 a0 a2 a1 a0 a2

25. Schrödinger equation Solving the one-dimensional Schrödinger equation.

26. Schrödinger equationelectron in free space - E - E

27. Schrödinger equation - E - E

28. Schrödinger equation Infinite potential well

29. Schrödinger equation Three-dimensional Laplacian operator in Cartesian coordinates Separation of variables Three ordinary differential equations plus one algebraic equation

30. Integers called quantum numbers Pauli exclusion principle 2 electrons cannot have the same quantum numbers. Electron spin => +1/2 & -1/2 Schrödinger equation One particular boundary condition Algebraic equation

31. Schrödinger equation

32. Schrödinger equation Atoms approximately are three-dimensional spherical objects. Electron spin => +1/2 & -1/2 Trigonometric function Bessel function Legendre polynomial

33. Bessel function Legendre polynomial Schrödinger equation One can satisfy different boundary conditions. This leads to certain integers. Quantum numbers. Pauli exclusion principle 2 electrons cannot have the same quantum numbers.

34. Schrödinger equation Pauli exclusion principle 2 electrons cannot have the same quantum numbers. shell is filled!

35. Heisenberg uncertainty principle Particle slows down - conservation of energy - photo electric effect Deviation must be greater than the wavelength http://www.aip.org/history/heisenberg/