1. 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
HW setup
Looking ahead: spectra workshop this Thus. afternoon in Homeroom (may move to CAL later)

2. 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)

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

4. 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

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

6. 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 =

7. 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._) # _

8. Phys.B: Early atomic models

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

10. 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.

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

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

13. 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