Electronic Structure of Atoms

1. Electronic Structure of Atoms

2. Wave Nature of Light section 6.1 • Much of what we know about electrons in atoms came from analyzing light that is emitted or absorbed by substances, so it figures that to understand electrons better, understanding light better would help. • Electromagnetic radiation=radiant energy=“light” • All types travel through space/vacuum at 3.00x108m/s, the speed of light, c. All types have wavelike properties.

4. Electromagnetic radiation • Inverse relationship between wavelength, λ, and frequency, ν. • C = νλ • What’s new? C over lambda. Ha ha. • This means that the product of wavelength and frequency is always 3.00 x 108 m/s. • Unit for λ is meters. • Unit for ν is s-1, “per second”, or Hz.

6. What does this have to do with electrons? • Three phenomena in nature could not be explained using the wave model of light, and as physicists explained them, their explanations spilled into the electron world as well. • 1. Blackbody radiation • 2. Photoelectric effect • 3. Emission spectra of elements

7. 1. Blackbody Radiation section 6.2 • A heated object gives off light, and the hotter it gets the wavelengths and intensity change. • In 1900, Max Planck proposes the idea of “quanta” of energy: energy is released/absorbed in discrete “chunks” of some minimum amount of energy. • This energy, E, is a constant times the frequency of the radiation emitted. E = hν • H is Planck’s constant: 6.626 x 10-34 J-s • Energy can only be emitted/absorbed in whole-number multiples of hν. (2hν, 3hν, 4hν, etc.) • Quantized energy is proven true, Planck receives 1918 Nobel for physics.

8. The color and intensity of the light emitted by a hot object depend on the temperature of the object. The temperature is highest at the center of this pour of molten steel. As a result, the light emitted from the center is most intense and of shortest wavelength.

9. 2. Photoelectric Effect • Light, of a certain minimum frequency, shining on a piece of metal will cause electrons to leave the metal, creating a voltage. • Photoelectric Effect - Light, Quantum Mechanics, Photons - PhET • Einstein interprets this as light acting not as a wave, but as a stream of particles of energy. He calls these energy particles photons, and that every photon contains an energy equal to Planck’s constant times the frequency of the light. Again, E = hν • So, is light a wave or a particle?

10. When photons of sufficiently high energy strike a metal surface, electrons are emitted from the metal

11. The photoelectric effect is the basis of the photocell shown in (b). The emitted electrons are drawn toward the positive terminal. As a result, current flows in the circuit. Photocells are used in photographic light meters as well as in numerous other electronic devices.

12. 3. Emission spectra and the Bohr modelsection 6.3continuous spectrum:

13. Emission spectra and the Bohr model • When the light from electrified elements passes through a prism, only a few wavelengths are present. This is a line spectrum.

14. Niels Bohr’s Explanation of Line Spectra • 1. Only orbits of a certain radii, corresponding to certain energies, are permitted for the electron. • 2. An electron in a permitted orbit has a specific energy and is in an “allowed” state. An electron in an allowed state will not radiate energy and therefore not fall into the nucleus. • 3. Energy is absorbed or emitted ONLY as the electron changes from one allowed state to another. This energy is absorbed/emitted as a photon, E = hν. (Flame test lab).

15. Energy States • Bohr calculated the energy of each allowed orbit, according to: • E = (-hcRH)(1/n2) or (-2.18 x 10-18J)(1/n2), where n is the principal quantum number (energy level) and is an integer starting with 1. • Each energy level will have a number, n, and an energy associated with it. • Ground state, n=1, is the lowest, or closest, orbit, and as n increases, the atom is said to be in an excited state.

16. ( ) 1 nf2 - E = −RH 1 ni2 The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: where RH is the Rydberg constant, 2.18  10−18 J, and ni and nf are the initial and final energy levels of the electron.

17. Energy states, cont. • The electron can “jump” from one energy state to another by absorbing or emitting a photon whose energy corresponds exactly to the energy difference between states. • Bohr’s model helped to explain the three phenomena mentioned earlier, but only with hydrogen atoms, and it too had shortcomings. • A completely new understanding of matter was necessary…..

18. Matter as Waves section 6.4 • So Einstein described light as being a wave with particle-like properties, depending on the situation. • Bohr described the electron as being able to absorb or emit photons which possessed a certain energy or frequency (hν). • In the 1920’s, Louis deBroglie suggests that perhaps the electron travels around the nucleus at a particular wavelength, and that the wavelength of the electron, or anything, depended on its mass. • λ = h/mv

19. Matter as Waves • λ = h/mv can be applied to any object, but the mass of a normal everyday object would cause the wavelength to be absurdly small. • Not long after this idea is proposed, a beam of electrons is experimentally shown to move, deflect, and behave like a wave of electromagnetic radiation (“light”).

20. The Uncertainty Principle • Developed by Werner Heisenberg in the early 1920’s in response to deBroglie’s wave ideas, it says, put simply, that with matter moving in wave motion, it is impossible to know both the momentum and position of an electron at any one time. We can determine one or the other, but never both. • And so, in 1926, Erwin Schrodinger invents quantum mechanics, a field of mathematics that will describe the electron’s behavior beautifully, but also shatter how we think about the world.