Inside the Modern Atom

Review of Waves Properties:

Wavelength (): distance between two successive crests Frequency (f): number of wave crests passing per second Speed of wave: v=f Amplitude (A): maximum displacement Energy: E A2

Interference

Only waves experience interference this is just adding up the parts of a wave:

Where two crests (or troughs) meet, they add

Where a crest and trough meet, they cancel

Light: Particles vs. Waves Light was originally thought to be a particle

E.g., look at sharp shadows, photoelectric effect, etc. also, Newton endorsed the view that light was made up of particles

Particles behave completely differently when they encounter slits...

E.g., suppose you fired bullets at one slit? What does that look like? Just a simple curve...

What if you fired bullets at two slits? Just two separate curves

So what happens when you fire light at it? Interference like water waves!

The Photoelectric Effect• When light hits certain metals, e- are ejected •Only the frequency (color) of the light affected the energy of the ejected e- • Higher frequency light ejected e- with higher energy

The Atomic Spectra

Light from bulbs, stars, etc. show a continuous spectrum when seen through a prism

A hot gas, however, has an emission line spectrum made of a few, discrete lines of color

Why don't hot gases show continuous spectra?

Absorption

Emission

Quantum Hypothesis: Energy is quantized What is quantization? It only comes in discrete chunks

instead of a continuous range of energies Planck suggested Energy is quantized in units of h and was

proportional to the oscillators frequency: E = hf

Continuous Discrete

Quantum Hypothesis: Light is quantized Einstein proposed that light is also quantized and its energy

is also determined by its frequency via E = hf Each individual packet of light energy is called a photon and

an EM wave is made of these individual "particles" Brighter light → more photons strike metal each second →

more e- ejected/sec (but it does not increase the energy of each e-)

Higher frequency light ejects e- with more energy because each photon has more energy to give

E hf346.626 10 J sh

maxK hf

Structural Models of the Atom

2

200 02ar r

Ze

e

Thompson “Plumb Pudding” Model

Bohr “Planetary” Model QM “Probability” Model

Rutherford “Point Nucleus” Model

Aristotle’s “Point” Model

Quantum Hypothesis: Orbits are quantized Bohr suggested that the orbits of electrons are also quantized An electron can go from one level to another by absorbing or emitting a

photon of light If light energy is quantized and electron orbits are also quantized, that

would explain why atomic spectra are discrete (since atoms/electrons only absorb or emit a single photon at a time)

The Bohr Model of the Hydrogen Atom

Bohr’s Quantum Conditions

I. There are discrete stable “tracks” for the electrons. Along these tracks, the electrons move without energy loss.

II. The electrons are able to “jump” between the tracks. In the Bohr model, a photon is

emitted when the electron drops from a higher orbit (Ei) to a lower

energy orbit (Ef).

Ei-Ef=hf

Predicted Energy Levels Instead of looking at orbits, we now look at energy

levels, which are the certain, allowed energy states Lowest energy level (corresponding to innermost

orbit in Bohr theory) is called the ground state and higher energy states are excited states

The structure of the atom is shown schematically on an energy-level diagram labeled with a quantum number n

As quantum number ↑, Energy associated with that state ↑

Transition of the electron from one orbit to another is now represented as the atom going from one energy level to another

Transition achieved by absorption or emission of a photon with an energy corresponding to the difference in energy between the two levels, or states When white light hits an atom, only photons with the

right energy are absorbed!

Energy, Light, & Orbits are quantized!

This is why it's called quantum mechanics: everything is quantized (comes in discrete chunks instead of a continuous range of values) -- matter (the Bohr "orbitals"), light, and even energy are ALL quantized!

DeBroglie further hypothesized that since electrons also behave as waves, they must also have a wavelength: λ = h/mv electron

wave

de Broglie Waves in the Hydrogen Atom

In this example, three complete wavelengths are contained in the circumference of the orbit

In general, the circumference must equal some integer number of wavelengths 2 r = n λ ; n = 1, 2, …

Heisenberg Uncertainty Principle Heisenberg proposed that the wave aspect of an electron

makes it impossible to know both the position and momentum to arbitrary precision

Heisenberg Uncertainty Principle (HUP): Δx • Δ(mv) ≥ h/4π

E.g., if you have a periodic wave (or a standing wave) you can't really tell what its position is (it's spread out over the whole string, e.g.). But you can tell exactly what its wavelength is. Now if you send a wave pulse down the string, you can't tell what its wavelength is (doesn't make sense for a pulse) but you can tell exactly what its position is.

The Atomic Structure So we can't say where exactly the electron is (it's not like a billiard ball,

or like a wave, or like a puffy cloud, or like anything else we know from ordinary experience)

"Now we know how the electrons and light behave. But what can I call it? If I say they behave like particles I give the wrong impression; also if I say they behave like waves. They behave in their own inimitable way, which technically could be called a quantum mechanical way. They behave in a way that is like nothing that you have ever seen before. Your experience with things that you have seen before is incomplete. The behavior of things on a very tiny scale is simply different. An atom does not behave like a weight hanging on a spring and oscillating. Nor does it behave like a miniature representation of the solar system with little planets going around in orbits. Nor does it appear to be somewhat like a cloud or fog of some sort surrounding the nucleus. It behaves like nothing you have ever seen before." -- Richard P. Feynman, The Character of Physical Law

Since we can't talk about its exact location, it's more useful to concentrate on the electron's energy

Some Atomic Physics Atom can gain or lose energy by absorption or

emission of photons or by collisions Pauli Exclusion Principle: two electrons cannot occupy

the same quantum state at the same time Number of quantum states in a given energy level

given by 2n2 If even one electron is in a higher energy level, the atom

is said to be in an excited state

Properties of each element determined by the ground-state configuration of its atoms (e.g., valence electrons, etc.)

Four Known Forces Two familiar kinds of interactions:

gravity (masses attract one another) and electromagnetism (same-sign charges repel,

opposite-sign charges attract) What causes radioactive decays of nuclei ?

Must be a force weak enough to allow most atoms to be stable.

What binds protons together into nuclei ? Must be a force strong enough to overcome

repulsion due to protons’ electric charge

Previously, we peered inside the atom

We recalled that electrons orbit the atom’s massive nucleus and determine an element’s chemical behavior.

We explored the proton and neutron content of nuclei and the phenomena of radioactivity, fission, and fusion they make possible. Today we’ll look inside the

nucleons themselves. Fundamental particles in the

Standard Model are: Leptons Quarks Intermediate Gauge Bosons

Anti-matter

Each kind of elementary particle has a counterpart with the same mass, but the opposite electric charge, called its “anti-particle”. Electron: m= .0005 GeV, charge = +1, symbol e-

Positron: m = .0005 GeV, charge = -1, symbol e+

The anti-particle has a bar over its symbol: Anti-proton is written , anti-neutrino is

Anti-matter is rare in the explored universe It’s created in cosmic rays and particle accelerators

and some radioactive decays. When a particle and its anti-particle collide, they

“annihilate” one another in a flash of energy.

p

v

Stability diagramHeavy elements can fissioninto lighter elements.

Light elements can undergofusion into heavier elements.

Elements from helium to iron were manufactured in the cores of stars by fusion. Heavier elements are metastable and were made during supernovae explosions.

Chain reaction

For reaction to be self-sustaining, must haveCRITICAL MASS.

Fusion Light nuclei are more stable when

combined Tremendous energy released Hydrogen bombs and Fusion

power?