Chapter 2 Atomic Structure

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

7. 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)

9. 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?

11. 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)

13. 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.

14. 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?