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

Problems with the Rutherford Atom Acceleration/Radiation Spectral Lines

Rydberg’s Formula: (FYI) Spectral lines Energy from excited atoms demo Rydberg’s Formula: (FYI) 1/ = R(1/22 - 1/n2), n = 3, 4, ...(Balmer) (Visible) 1/ = R(1/12 - 1/n2), n = 2, 3, ...(Lyman) (UV) 1/ = R(1/32 - 1/n2), n = 4, 5, ...(Paschen) (IR) (R = 1.097 x 10-7 m-1) H He Sun

Bohr’s Quantum Atom Assumptions of Bohr’s model: 1. Only certain orbits are allowed “stationary states” 2. Electron transitions between states create photons:

Example 1: 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

3. Angular Momentum is Quantised: (show that mvr = I…..but why????) Example 2: Show that mvr is angular momentum (L = I)

Ultimately, the energy levels can be simplified to this expression. Book derives it – triumph of HS algebra Why is it negative? Example 3: What is the energy level of the 4th orbital, and the 2nd orbital? What wavelength of light corresponds to a 4 to 2 transition for a Hydrogen atom? (The 2nd Balmer line)

Whiteboards: Bohr Photons 1 | 2 | 3 | 4

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

What is the wavelength of the photon released from the third Lyman spectral line (from -0.85 to -13.6 eV)? 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 97 nm

What is the wavelength of the photon released from the second Balmer spectral line (from –0.85 to -3.4 eV)? 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 490 nm

An 102.5 nm photon is emitted. What is the energy of this photon in eV, and what transition occurred? 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 12.1 eV

What is the energy of the n = 5 orbital? What is the wavelength of the photon released from a 5 to 3 transition? (Hydrogen atom) solution -0.544 eV, -1.51 eV, 1.28x10-6 m

What is the wavelength of the photon released from a 4 to 1 transition What is the wavelength of the photon released from a 4 to 1 transition? (Hydrogen atom) solution 97.3 nm

Quantisation of Angular Momentum Why are only certain orbits allowed? (demo) Circumferences of Bohr orbits are integer multiples of de Broglie wavelength

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

Limitations of Bohr’s model 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