Physics of Astronomy Tuesday, winter week 8 (28 Feb.06) 12:30 Math-A: Giancoli – Ch. 8 Energy, Ch.14 Oscillations 2:30 Discuss research presentations next week Math-B: Bohr atom: Giancoli 38, Raff Ch.11.2.4-6 HW setup Looking ahead: spectra workshop this Thus. afternoon in Homeroom (may move to CAL later)

Forces do work and change energy Work done = force . displacement in the same direction, Fx= -dU/dx Ex: Gravity: F = mg, W = Ex: Spring: F = -kx, Conservation of mechanical energy: Etot = K + U = constant Conservative force: Work done doesn’t depend on path taken (curl x F = 0)

Gravitational potential energy and force Near earth far from Earth Force F Potential energy U

Ch.8-8,9: Energy diagrams and Power Power = rate of change of Energy P = dE/dt Minimum energy = stable state (F=0) Ch.8 (Power, 203) #57, 59, 62, 65, 67, (Diag) 68-71, 94-97

Ch.14: Oscillations Systems oscillate about energy minimum Ex: Spring oscillates about equilibrium x0 Displacement x(t) = A cos (wt + f) Ch.14 (p._) # _

Energy in Oscillations Displacement x(t) = A cos (wt + f) Speed v = dx/dt = Potential energy U(t) = ½ kx2 = Kinetic energy K(t) = ½ mv2 =

Frequency of oscillation of spring Angular frequency = angular speed = w = 2pf where frequency f = 1/T and T = period. Differentiate: Simplify: Solve for w2: Ch.14 (p._) # _

Phys.B: Early atomic models

Observed spectra of Hydrogen and other elements Calculate energies of H lines from their colors: E = hc/l Planck constant h = 6.63 x 10-34 J.s Energy units: 1 eV = 1.602 x 10-19 J

Electrons as waves (1923) DeBroglie postulated: if light can behave like a particle (E = hc/l= pc) then maybe matter could behave like waves! What would be an electron’s wavelength? h/l = p = mv Integer # wavelengths = circumference nl = 2pr mv = L = mvr = Quantization of angular momentum! (1927) Davisson and Germer discovered that electrons can diffract as waves! thanks to an accident with their nickel crystal.

Bohr model for the Hydrogen atom Solve for (1) v2= Solve mvr = nh/2p for (2) v2= Equate v2=v2: Solve for r

Energy levels of Bohr atom Calculate H energy levels from theory Compare to energies of observed spectral lines They match!

Bohr’s synthesis: Bohr combined Rutherford’s model of the orbiting electron with deBroglie’s hypothesis of electron wavelengths: angular momentum would be quantized in electron orbits Derived orbit radii and energy levels for H-like atoms. Despite unanswered questions (such as how could such orbits be stable?), Bohr’s model fit observations: * Balmer spectrum * Rydberg constant