1 / 16

Chapter 2 Atomic Structure

Chapter 2 Atomic Structure. HW: 1, 3, 11, 13, 17, 20, 24, 25, 30, 32, 33, 39, 40 The Periodic Table The Bohr Atom The Schrodinger Equation Orbitals Shielding Periodic Properties of Atoms. Subatomic Particles.

Download Presentation

Chapter 2 Atomic Structure

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.


Presentation Transcript

  1. Chapter 2Atomic Structure • HW: 1, 3, 11, 13, 17, 20, 24, 25, 30, 32, 33, 39, 40 • The Periodic Table • The Bohr Atom • The Schrodinger Equation • Orbitals • Shielding • Periodic Properties of Atoms

  2. Subatomic Particles • 1885 - Balmer derived a formula to calculate the energies of visible light emitted by the hydrogen atomn = integer, > 2R = Rydberg constant for hydrogen = 1.097 x 107 m–1 • General version of the equation: n = principal quantum number, nl < nh • Origin of energy unknown until Bohr’s atomic theory (1913) derived same equation. R = fundamental constant = Connection between experiment and theory

  3. Bohr’s Atomic Theory • Negatively charged electrons orbit the positively charged nucleus • When energy is absorbed, electrons move to higher orbits • When electrons move to lower orbits, energy is emitted • Equation predicted line spectra onlyfor single-electron atoms • Adjustments were made to use elliptical orbits to better fit data • Ultimately failed - did not incorporate wave properties of electrons. Still a useful theory.

  4. Quantum Mechanics • Particles as waves(de Broglie) • Uncertainty principle(Heisenberg)Electrons - energy can be measured very accurately, therefore cannot know position (x) with any certainty • Probability of finding an electron at any position(electron density = probability) • Both Schrodinger and Heisenberg proposed ways to treat electrons as waves, Schrodinger’s math was easier

  5. Wave Functions • H= E  , where H operates on . • Solutions to equation are wave functions, each corresponding to an atomic orbital • The conditions for a physically realistic solution:-One value for electron density/point-Continuous (does not change abruptly)-Must approach zero as r approaches infinity-Normalized (total probability = 1)-Orthogonal

  6. Atomic wave functions • Solving equations requires 3 quantum numbers: n, , m • n - principal (size and energy) - angular momentum (shape, contributes to energy)m - magnetic (orientation)ms - spin (orientation of electron spin) • Plot in 3-D space (spherical coordinates), need 3 variables: , r,  • Break wavefunction into radial function (R), electron density at distances from nucleus, and angular function (, ), shape of orbital and orientation in space • R(r)·Y(, ) = R(r)· Y(x,y,z)

  7. Angular Functions, Y(x,y,z) • Table 2.3 • Determine how probability changes at a given distance from the center of the atom (shape and orientation in space) • Look at real wave functions, in Cartesian coordinates • Where do orbital labels come from? • Why are some regions shaded?

  8. Radial Functions, R(r) • Table 2.4 • 1s: n = 0,  = 0a0 = Bohr radius (radius of first “orbit” for H atom)= 52.9 pm • Three ways to look at radial function:R vs. rR2 vs. r (probability)4r2R2 vs. r (radial probability density)

  9. Radial Probability Density • 4r2R2: probability of finding electron at a given distance from nucleus, summed over all angles • Probability of finding the electron at a certain distance from the nucleus is not equal to the probability of finding the electron at a certain point at that distance from the nucleus. • There is a whole surface of a sphere on which we can find the electron at that distance, r. • 1s orbital: radial probability function has a maximum at r = a0 (Bohr radius). This is the distance from the nucleus where the electron in a 1s orbital is most likely found.

  10. Homework Assignment • Orbital plots (use Excel) for 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f orbitals (you have to find the equations for the n=4 orbitals) (Orbitron!) • Plot R, R2, and r2R2 (each as a function of )Print all plots, showing function approaching zero as  increases • See Figure 2.7 for n = 1 to n = 3, R and r2R2 plotsDue date?

More Related