Bohr’s Atomic Model Suggested________________________________ and that the electrons ________________________________________ electrons can only be in discrete orbitals Absorb or emit energy as they move between orbitals

ΔE = E3-E1 = hv Bohr’s Atomic Model As electrons move between orbits, their PE/KE is transformed into radiation (photon) The difference in energy between orbits is equal to the energy of a photon ΔE = E3-E1 = hv Energy gained/lost by e- Energy of a photon absorbed/ released E3 E1

𝑚 𝑒 𝑣 2 𝑟 =k 𝑍𝑒 𝑒 𝑟 2 v e r Z: number of protons (Ze) Bohr’s Atomic Model Where can the electrons be??? Bohr modeled the electrons as orbiting the nucleus, in contrast to the classical physics description of charged particles. Condition of Stability……. 𝑚 𝑒 𝑣 2 𝑟 =k 𝑍𝑒 𝑒 𝑟 2 The electron must move fast enough so that The________________ equals the electromagnetic force between the electron and nucleus v e centripetal force Classical physics noted that when charge particle more relative to one another they emit energy (light). Electrons would lose kinetic energy and crash into the nuceuls. r Z: number of protons e: fundamental charge (1.60x10-19) coulombs r: radius v: speed (Ze)

Bohr’s Atomic Model Bohr modeled that electrons were in orbits…… But how do we explain discrete emission spectrum from atoms? Bohr suggests__________________________________________________________ __________ angular momentum of electron must equal some integer (n) multiple of Plank’s constant As a result….. the radii of the orbits are quantized… (can only have specific values)

n = the discrete orbital angular momentum of electron must equal some integer (n) multiple of Plank’s constant n = 3 n = the discrete orbital n = 2 n = 1

𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 n = 3 n = the discrete orbital n = 2 n = 1 Can solve for the the radii of the orbitals 𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 n = 3 n = the discrete orbital n = 2 n = 1

𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 ∞ Quantized Radii Hydrogen: Z = ______ For n = 1, r = 0.529 x 10-10 m For n = 2, r = 2.12 x 10-10 m For n = 3, r = 4.76 x 10-10 m For n = 4, r = 8.46 x 10-10 m . For n = ∞, r = ______________________ For hydrogen… 𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 1 0.52910-10 m 1.5910-10 m 2.6410-10 m 3.7010-10 m As n increase the radii get further apart ∞ As the integer (n) approaches infinity, the radii approaches infinity.

Bohr’s Atomic Radii for Hydrogen (Z=1) and Helium (Z=2) 𝑟=𝐶 𝑛 2 𝑍𝑒 𝑒 = 𝐶 𝑒 2 𝑛 2 𝑍 As Z increase r decreases! n = 1, r = 0.521 Ǻ n = 2, r = 2.13 Ǻ n = 3, r = 4.78 Ǻ n = 4, r = 8.50 Ǻ n = 5, r = 13.3 Ǻ n = 6, r = 19.1 Ǻ n = 7, r = 26.0 Ǻ n = 1, r = 0.267 Ǻ n = 2, r = 1.06 Ǻ n = 3, r = 2.39 Ǻ n = 4, r = 4.25 Ǻ n = 5, r = 6.64 Ǻ n = 6, r = 9.50 Ǻ n = 7, r = 13.0 Ǻ

How do we find the energy of an electron? With the position of the e- known we can determine the energy of it We don’t know how fast the e- is moving (v)…. But we can manipulate the variables and combine terms to get energy in terms of r. get

Quantized energy states The energy depends on where the electron is. If the radii are quantized (discrete) , the energies will be as well get (bunch o’ constants)

Difference in energy between two states (orbits), n1 and n2 Solve for E n1 n2 6 2 5 4 3 n2 = orbit where electron ends up n1 = orbit where electron starts

Ephoton= h𝜈 c= 𝜆𝜈 Predictions from Bohr’s model Transition n1 → n2 Energy Photon Energy Frequency Wavelength 6 → 2 5 → 2 4 → 2 3 → 2 -4.84x10-19 J 4.84x10-19 J 7.30x1014 1/s 4.11x10-7 m -4.58x10-19 J 4.58x10-19 J 6.91x1014 1/s 4.34x10-7 m -4.09x10-19 J 4.09x10-19 J 6.17x1014 1/s 4.86x10-7 m -3.03x10-19 J 3.03x10-19 J 4.15x1014 1/s 6.56x10-7 m The predicted and observed match up! Bohr’s model is correct…….. For Hydrogen

What about the data for Helium…. Bohr’s Atomic Radii for Hydrogen (Z=1) and Helium (Z=2) n = 1, r = 0.521 Ǻ n = 2, r = 2.13 Ǻ n = 3, r = 4.78 Ǻ n = 4, r = 8.50 Ǻ n = 5, r = 13.3 Ǻ n = 6, r = 19.1 Ǻ n = 7, r = 26.0 Ǻ n = 1, r = 0.267 Ǻ n = 2, r = 1.06 Ǻ n = 3, r = 2.39 Ǻ n = 4, r = 4.25 Ǻ n = 5, r = 6.64 Ǻ n = 6, r = 9.50 Ǻ n = 7, r = 13.0 Ǻ . What about the data for Helium….

 Don’t’ worry Neils…. it’s Formative Bohr’s Atomic Radii (n = 1 to 12) for Helium (Z=2) n = 1, r = 0.267 Ǻ n = 2, r = 1.06 Ǻ n = 3, r = 2.39 Ǻ n = 4, r = 4.25 Ǻ n = 5, r = 6.64 Ǻ n = 6, r = 9.50 Ǻ n = 7, r = 13.0 Ǻ n = 8, r = 17.0 Ǻ n = 9, r = 21.5 Ǻ n = 10, r = 26.6 Ǻ n = 11, r = 32.1 Ǻ n = 12, r = 38.3 Ǻ n = 13, r = 44.9 Ǻ Actual spectrum Predicted transitions in the visible and NOT observed  . . The predicted and observed DON’T match up  Bohr’s model is __________________ NOT correct!!! Don’t’ worry Neils…. it’s Formative