# Aim: How can we explain energy transitions in an atom? Do Now: What were the limitations of the Rutherford model of the atom and how did the Bohr model.

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Aim: How can we explain energy transitions in an atom? Do Now: What were the limitations of the Rutherford model of the atom and how did the Bohr model explain these limitations?

Emission Spectra When electron falls from higher to lower level, photon is emitted. Shows as bright series of lines.

Visible spectrum

Balmer Series Named after Johann Jacob Balmer 1825-1898

Gas Tube Demo

Energy of final level Energy of initial level Energy of photon emitted or absorbed

Calculate the energy of the photon emitted when a hydrogen atom changes from energy state n = 3 to n= 2, in eV and Joules E photon = E i – E f E photon = -1.51 eV – (-3.40 eV) E photon = 1.89 eV 1.89 eV * 1.60 x 10 -19 J = 3.0x10 -19 J 1 eV

For a mercury electron transition from level c to a, calculate E photon, λ, f, and the type of EM wave emitted. E photon = E i – E f E photon = -5.52 eV – (-10.38 eV) E photon = 4.86 eV 4.86 eV * 1.60 x 10 -19 J = 7.77 x 10 -19 J 1 eV

c= fλ 3.00 x 10 8 m/s = f (2.56 x 10 -7 m) f = 1.17 x 10 15 Hz This is ultraviolet light E photon = hc λ 7.77 x 10 -19 J = (6.63x10 -34 Js)(3 x 10 8 m/s) λ λ = 2.56 x 10 -7 m

An electron in a hydrogen atom drops from n = 4, n = 2. Find E photon (eV and Joules), f, and the color of light. E photon = E i – E f E photon = -0.85 eV – (-3.40 eV) E photon = 2.55 eV 2.55 eV * 1.60 x 10 -19 J = 4.08 x 10 -19 J 1 eV

E photon = hf 4.08 x 10 -19 J = (6.63 x 10 -34 Js)f f = 6.15 x 10 14 Hz This is blue light

Calculate the energy of the photon needed when a hydrogen atom changes from n =1 to n =∞ E photon = E i – E f E photon = -13.60 eV – 0.00 eV E photon = -13.60 eV

Ionization Potential Minimum energy needed to remove an electron from the ground state to infinity For hydrogen  -13.6 eV For mercury  -10.38 eV

A positive photon energy indicated photon is emitted A negative photon energy indicates photon is absorbed

Absorption Spectra When electron jumps to a higher energy level a photon is absorbed. Shows up as a series of dark lines.

Wave Model After De Broglie proposed matter waves, he was able to show the Bohr model could be explained by considering the orbits of a series of waves

Cloud Model (Shrödinger’s Model) Quantum mechanics indicates the probability of the electron being in a certain area Most probable regions are in area called ‘electron cloud’ Energy levels of Bohr model are divided into sublevels and orbitals -- together with Cloud model define the current model Erwin Shrödinger 1887-1961

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