2. Niels Bohr and the quantum atom Contents: Problems in nucleus land Spectral lines and Rydberg’s formula Photon wavelengths from transition energies Electron in a box Schrödinger Limitations of Bohr’s model Niels Bohr 1881 - 1962

3. Problems with the Rutherford Atom TOC Acceleration/Radiation Spectral Lines

4. Spectral lines Energy from excited atoms demo H He Sun TOC Rydberg’s Formula: (FYI) 1 / = R( 1 / 2 2 - 1 / n 2 ), n = 3, 4,...(Balmer) (Visible) 1 / = R( 1 / 1 2 - 1 / n 2 ), n = 2, 3,...(Lyman) (UV) 1 / = R( 1 / 3 2 - 1 / n 2 ), n = 4, 5,...(Paschen) (IR) (R = 1.097 x 10 -7 m -1 )

5. Bohr’s Quantum Atom Only certain orbits are allowed “stationary states” Electron transitions create photons 1 / = R( 1 / 2 2 - 1 / n 2 ), n = 3, 4,...(Balmer) (Visible) 1 / = R( 1 / 1 2 - 1 / n 2 ), n = 2, 3,...(Lyman) (UV) 1 / = R( 1 / 3 2 - 1 / n 2 ), n = 4, 5,...(Paschen) (IR)

6. Example: What is the wavelength of the first Lyman line? The first Lyman line is a transition from -3.4 eV to -13.6 eV, so it releases 10.2 eV of energy. A photon with this energy has this wavelength: E = (10.2)(1.602E-19) = 1.63404E-18 J E = hc/λ, λ = hc/E = (6.626E-34)(3.00E8)/(1.63404E-18) = 1.21649E-07 m = 122 nm

7. Whiteboards: Bohr Photons 11 | 2 | 3 | 42 TOC

8. What possible photon energies can you get from these energy levels? (there are 6 different ones) -14.0 eV -9.0 eV -6.0 eV -5.0 eV 1, 4, 9, 3, 8, and 5 eV 1 4 9 38 5

9. 97 nm W E = hf = hc/ E = -.85 - -13.6 = 12.75 eV E = (12.75 eV)(1.602E-19J/eV) = 2.04E-18J = hc/E = 97.3 = 97 nm What is the wavelength of the photon released from the third Lyman spectral line (from -.85 to -13.6 eV)?

10. 490 nm W E = hf = hc/ E = -0.85 -3.4 = 2.55 eV E = (2.55 eV)(1.602E-19J/eV) = 4.09E-19J = hc/E = 487 = 490 nm What is the wavelength of the photon released from the second Balmer spectral line (from –0.85 to -3.4 eV)?

11. 12.1 eV W E = hf = hc/ (6.626E-34)(3.00E8)/(86.4E-9) = 2.30069E-18 J (2.30069E-18 J)/(1.602E-19) = 12.1 eV This could be the second Lyman line An 102.5 nm photon is emitted. What is the energy of this photon in eV, and what transition occurred?

12. “Electron in a box” TOC Why are only certain orbits allowed? (Demo)

13. 6 x 10 -18 J W E k = 1 2 (6.626E-34) 2 /(8(9.11E-31)(.1E-9) 2 ) = 6.02413E-18 J (≈ 38 eV) Try this: What would be the kinetic energy of an electron in the ground state of a “box” that is about 0.1 nm in length? m e = 9.11x10 -31 kg

14. Schrödinger and the quantum atom TOC Schrödinger solves  for hydrogen atom The electron is represented by a wave Can only be solved for H, singly ionised He

15. Limitations of Bohr’s model TOC Works well for H, but doesn’t even work for He Did not explain Spectral fine structure Brightness of lines Molecular bonds Theory was not complete. But otherwise it generally kicked tuckus