“wave-particle duality” Quantum Theory Einstein (1905) Concluded - light has properties of both waves and particles “wave-particle duality” Photon - particle of light that carries a quantum of energy In 1905, Einstein returned to Newton’s idea of particles on light. Einstein proposed that light could be described as quanta of energy that behave as if they were particles. Light quanta are called photons. The energy of photons is quantized according to E = hv. The dual wave particle behavior of light was difficult for scientists to accept.

Quantum Theory The energy of a photon is directly proportional to its frequency. E = h Einstein recognized that there is a threshold value of energy below which the effect does not occur. If frequency is too low, no photoelectrons will be ejected. Solar powered calculators E: energy (J, joules) h: Planck’s constant (6.63  10-34 J·s) : frequency (Hz or 1/s)

Quantum Theory E = ? E = h  = 4.57  1014 1/s EX: Find the energy of a red photon with a frequency of 4.57  1014 Hz. GIVEN: E = ?  = 4.57  1014 1/s h = 6.63  10-34 J· s WORK: E = h E = (6.63  10-34 J· s) (4.57  1014 1/s) E = 3.03  10-19 J

End of Notes – Day 1

II. Bohr Model of the Atom Unit 3 – Modern Atomic Theory & the Periodic Table Modern Atomic Theory II. Bohr Model of the Atom

Review of Earlier Models Thomson’s Plum Pudding Model

Review of Earlier Models Rutherford’s Nuclear Model

Continuous Spectrum Results when white light is passed through a prism (like rainbow) Contains all wavelengths of visible light Another important experiment about the atom was the study of emission of light by excited hydrogen atoms. However, before we can understand the significance of this experiment, we must first describe the continuous spectrum.

Line-Emission Spectrum The spectrum produced by a gas (following an electric discharge) contains only a few wavelengths and some of the wavelengths are missing. This is called a Line-Emission Spectrum. Each element has its own spectrum.

Line-Emission Spectrum excited state ENERGY IN PHOTON OUT When a sample of hydrogen gas receives a high energy spark, the H2 molecules absorb energy, and some of the H-H bonds are broken. The resulting hydrogen atoms are excited; that is, they contain excess energy, which they release by emitting light of various wavelengths to produce what is called the emission spectrum of the hydrogen atom. When light is emitted, these atoms return to the ground state. In contrast to the continuous spectrum, we see only a few lines, each of which corresponds to a discrete wavelength. The hydrogen emission spectrum is called a line spectrum. What is significant about the line spectrum of hydrogen? It indicates that only certain energies are allowed for the electron in the hydrogen atom. In other words, the energy of the electron in the hydrogen atom is quantized. This observation fits perfectly with Planck’s and Einstein’s postulates. ground state

An Excited Lithium Atom Excited Li atom Energy Photon of red light emitted Li atom in lower energy state

A Change Between Two Discrete Energy Levels Changes in energy between discrete energy levels in hydrogen will produce only certain wavelengths of emitted light. If any energy level were allowed, the emission spectrum would be continuous.

Bohr Model (1913) e- exist only in circular orbits with specific amounts of energy called energy levels e- travels in a circle because of attraction to the nucleus Therefore… e- can only gain or lose certain amounts of energy only certain photons are produced https://www.youtube.com/wa tch?v=GhAn8xZQ-d8 Aware of results just discussed, Bohr proposed a quantum model for the hydrogen atom. He proposed that the electron in a hydrogen atom moves around the nucleus only in certain allowed circular orbits. He calculated the radii for these allowed orbits by using the theories of classical physics and by making some new assumptions.

Bohr Model (Planetary Model) Increasing energy of orbits n = 3 e- n = 2 n = 1 e- e- A photon is emitted with energy E = h Bohr proposed that electrons travel in definite orbits around the nucleus. 14

Bohr’s Model Nucleus Electron Orbit Energy Levels 15

Bohr Model Energy of photon depends on the difference in energy levels 6 Energy of photon depends on the difference in energy levels Bohr’s calculated energies matched the IR, visible, and UV lines for the H atom 5 4 3 2 1 Uses Rutherford’s Model with Planck’s idea of “quantized” energy

Problems with the Bohr Model His calculations only worked for hydrogen! According to classical physics, light should be emitted as the electron circles the nucleus. A loss of energy would cause the electron to be drawn closer to the nucleus and eventually spiral into it. Emission spectrum can be used to identify elements. When Bohr’s model was applied to atoms other than hydrogen, it did not work at all. It was concluded that Bohr’s model was fundamentally incorrect but it did pave the way for later theories.

Application: Fireworks

End of Notes – Day 2