Introduction to Modern Physics A (mainly) historical perspective on - atomic physics  - nuclear physics - particle physics

Theories of Blackbody Radiation Classical disaster ! Quantum solution

Planck’s “Quantum Theory” The “oscillators” in the walls can only have certain energies – NOT continuous!

The Photoelectric Effect Light = tiny particles! Wave theory: takes too long to get enough energy to eject electrons Particle theory: energy is concentrated in packets -> efficiently ejects electrons!

The Photoelectric Effect Energy of molecular oscillator, E = nhf Emission: energy nhf -> (n-1)hf  Light emitted in packet of energy E = hf Einstein’s prediction: hf = KE + W (work function)

c = f Speed of light 3 x 10 8 meter/second or 30cm (1 foot) per nanosecond Wavelength (meter) Frequency #vibrations/ second

hf = KE + W (work function)

The Photoelectric Effect Wave Theory Photon Theory Increase light intensity -> more electrons with more KE Increase light intensity -> more photons -> more electrons but max-KE unchanged ! Frequency of light does not affect electron KE Max-KE = hf - W If f < f(minimum), where hf(minimum) = W, Then NO electrons are emitted! X X

How many photons from a lightbulb? 100W lightbulb, wavelength = 500nm Energy/sec = 100 Joules E = nhf -> n = E/hf = E /hc  n = 100J x 500 x = 2.5 x !! 6.63 x J.s x 3 x 10 8 m/s

So matter contains electrons and light can be emitted in “chunks”… so what does this tell us about atoms?? Possible models of the atom Which one is correct?

Electric potential V(r) ~ 1/r The Rutherford Experiment

Distance of closest approach ~ size of nucleus At closest point KE -> PE, and PE = charge x potential KE = PE = 1/4  0 x 2Ze 2 /R R = 2Ze 2 / (4  0 x KE) = 2 x 9 x 10 9 x 1.6 x x Z 1.2 x J = 3.8 x Z meters = 3.0 x m for Z=79 (Gold)

The “correct” model of the atom …but beware of simple images!

Atomic “signatures” Rarefied gas Only discrete lines! An empirical formula! n = 3,4,…

The Origin of Line Spectra

Newton’s 2 nd Law and Uniform Circular Motion  F = ma Acceleration = v 2 /r Towards center of circle!

How do we get “discrete energies”? Linear momentum = mv Radius r Angular momentum L = mvr Bohr’s “quantum” condition – motivated by the Balmer formula

Electron “waves” and the Bohr condition De Broglie(1923): = h/mv Only waves with a whole number of wavelengths persist Quantized orbits! n = 2  r Same!!

Electrostatic force: Electron/Nucleus COULOMBS LAW

Combine Coulomb’s Law with the Bohr condition: Newton’s 2 nd Law Circular motion 

(for Z = 1, hydrogen)

Calculate the total energy for the electron: Total Energy = Kinetic + Potential Energy Electrostatic potential Electrostatic potential energy

Total energy Substitute

So the energy is quantized ! … now we can combine this with

…and this correctly predicts the line spectrum for hydrogen, …and it gets the Rydberg constant R right! …however, it does not work for more complex atoms…

Experimental results

Quantum Mechanics – or how the atomic world really works (apparently!) De Broglie(1923): = h/mv Take the wave description of matter for real: Describe e.g. an electron by a “wavefunction”  (x), then this obeys: Schroedinger’s famous equation

Now imagine we confine an electron in a “box” with infinitely hard/high walls:

Waves must end at the walls so:

and the energy levels for these states are: Discrete energies!

The probabilities for the electron to be at various places inside the box are: vs. Classical Mechanics Uniform probability!

Applying the same quantum mechanical approach to the hydrogen atom: Probability “cloud” Bohr radius

The “n = 2” state of hydrogen:

Atomic orbitals

Weird stuff!!

Ghosts!!??

Conclusions - Classical mechanics/electromagnetism does not describe atomic behavior - The Bohr model with a “quantum condition” does better…but only for hydrogen - Quantum mechanics gives a full description and agrees with experiment - …but QM is weird!!