1. Absorption / Emission of Photons and Conservation of Energy E f - E i = hvE i - E f = hv hv

2. Energy Levels of Hydrogen

3. Electron jumping to a higher energy level E = 12.08 eV

4. Spectrum of Hydrogen, Emission lines Bohr’s formula:

5. Hydrogen is therefore a fussy absorber / emitter of light It only absorbs or emits photons with precisely the right energies dictated by energy conservation

6. Electron in a Hydrogen Atom The three quantum numbers: –n = 1, 2, 3, … –l = 0, 1, …, n-1 –m = -l, -l+1, …, l-1, l For historical reasons, l = 0, 1, 2, 3 is also known as s, p, d, f

7. 1s Orbital

8. Density of the cloud gives probability of where the electron is located

9. 2s and 2p Orbitals

10. Another diagram of 2p orbitals Note that there are three different configurations corresponding to m = -1, 0, 1

11. 3d Orbitals Now there are five different configurations corresponding to m = -2, -1, 0, 1, 2

12. 4f Orbitals There are seven different configurations corresponding to m = -3, -2, -1, 0, 1, 2, 3

13. The excited atom usually de-excites in about 100 millionth of a second. The subsequent emitted radiation has an energy that matches that of the orbital change in the atom. This emitted radiation gives the characteristic colors of the element involved.

14. Emission Spectra Continuous Emission Spectrum Prism Photographic Film Slit White Light Source

15. Emission Spectra of Hydrogen Prism Photographic Film Film Slit Low Density Glowing Hydrogen Gas Discrete Emission Spectrum

16. Portion of the Absorption Spectrum of Hydrogen Discrete Absorption Spectrum Prism Photographic Film Film Slit White Light Source Discrete Emission Spectrum Hot Hydrogen Gas

17. Absorption Spectra Frequencies of light that represent the correct energy jumps in the atom will be absorbed. When the atom de-excites, it may emit the same kinds of frequencies it absorbed. However, this emission can be in any direction.

18. Emission and Absorption Continous Spectrum Portion of the Emission Spectrum Absorption Spectrum Hot Gas Cold Gas

19. Absorption spectrum of Sun Emission spectra of various elements

21. Usually the Emission spectrum has more “features” of the absorption spectrum Atom excitation, Absorption lines from the ground state (n=1) Atom de-excitation, Emission lines from the excited states

22. Schrodinger equation for one electron atoms Coulomb potential

23. Radial and angular part

24. BORN POSTULATE The probability of finding an electron in a certain region of space is proportional to  2, the square of the value of the wavefunction at that region.  can be positive or negative.  2 is always positive  2 is called the “electron density” What is the physical meaning of the wave function?

25. E.g., the hydrogen ground state  1 1 3/2  1s = e -r/a o (a o : first Bohr radius=0.529 Å)  a o  1 1 3  2 1s = e -2r/a o  a o  2 1s r

26. Radial electron densities The probability of finding an electron at a distance r from the nucleus, regardless of direction The radial electron density is proportional to r 2  2 Surface = 4  r 2 rr Volume of shell = 4  r 2  r