Hydrogen atom energy levels deBroglie and Bohr got the spectrum right! 1. Wavelength comes from speed: 2. Integer wavelengths fit in orbit of size r 3. F = ma:

Light frequencies emitted/absorbed are given by initial and final electron energy levels

But Bohr got so much wrong… 1. Can’t give energies for anything but H atom. 2. Assumes planar orbits, while atoms are more spherical 3. The electrons are not at a single distance r 4. His ideas about angular momentum were too simple. The quantum state labels are not just n: they include l,m, and s.

Angular momentum in QM L Classical: any L, w, KE allowed Quantum: L, w, KE are quantized angular momentum magnitude l =0,1,2… orbital angular momentum quantum number l=0: “s” orbital in chemistry l=1: “p” orbital in chemistry l=2: “d” orbital in chemistry

Angular momentum in QM Lz quantum number Quantum: the component of L along any axis measured is also quantized (call the measurement axis z): Uncertainty: We can’t know the direction of L with precision. We can only know the z component. Lz quantum number m = -l…l there are 2l+1 values of m

Electron spin Besides orbital angular momentum, electrons have spin angular momentum We can know only the z component of the spin:

Clicker P1. What angle does the upper S cone make vs the z axis? _______ deg a) 25-35 b) 35-45 c) 45-55, d) 55-65 e) 65-75

Quantum states in atoms To illustrate how bad the idea of the electron “orbiting” the nucleus is, here is the lowest energy probability: Because l = 0, there is no angular momentum, so no circular motion about the nucleus, just motion radially

Quantum states in atoms Each electron quantum state is labeled by n,l,m,ms l can be (0 … n-1) chemistry: n=3, l=1,m=-1, ms=-1/2 would be 3p: _↓_ ___ ___ P2. Including spin, how many total electrons states are there for n = 3? Count all possible l,m,ms

Quantum states in atoms In H-atom, energy depends only on n In all other atoms, there is more than one electron, and electron repulsion makes each electron’s energy depend on all the other electrons: so state energy depends on n,l,m,ms Higher kinetic energy is associated with more peaks and nodes in the wavefunction, radially and angularly

Light and quantum states Absorption

Light and quantum states Florescence, phosphorescence

Florescent minerals

Fluorescent shirts They are brighter than other cloth because they don’t scatter much light…they convert much of the visible spectrum into a single color

Lasers Lase: Light Amplification by Stimulated Emission

Lasers Need many atoms in excited state (“Population inversion”). Photons bouncing between mirrors stimulate emission of other photons that match their phase, direction.

Laser level diagram To get a population inversion, need at least electron 3 levels, one of which is long-lived or “metastable” (as in flourescence)

Diode lasers Inject energetic electrons into semiconductors: light emitting diode or laser