PH 103

Dr. Cecilia VogelLecture 19

Review

Outline Uncertainty Principle

Tunneling Atomic model

Nucleus and electrons The quantum model quantum numbers

Matter Waves

Position Uncertainty A wave is not at

one place.x = uncertainty in

position = spread in positions

where the wave is.x

Momentum Uncertainty

A wave is not moving in just one way.

p = uncertainty in momentum

= spread in ways the wave moves.

p

Heisenberg Uncertainty Principle

What it means: You cannot know position and momentum

both very precisely at the same time If you measure momentum, you disturb

the position, so you no longer know the position accurately -- and vice versa

This disturbance is random, indeterminate

(unlike letting a little air out when you measure the tire pressure)

2

hpx x

Heisenberg Uncertainty Principle

2

hpx x

Heisenberg Uncertainty Principle

Zero-point motion: Any confined particle cannot have

a definite momentum in particular, it cannot have zero

momentum any confined particle will have

some kinetic energy -- some “zero-point motion”

2

hpx x

Heisenberg Uncertainty Principle

What it does not mean: It does not mean you can’t measure

position (or momentum) very precisely. It does not mean you need better

measuring instruments. It does NOT just a matter of not

knowing:If x is large enough, an electron will pass

thru both of two slits

2

hpx x

and interfere with itself

Another Uncertainty Principle

What it means If you only have a small time t to

measure energy, you can’t accurately measure energy.

If a particle only lives for a short time t, you can’t accurately measure its energy. Since E=mc2, you can’t accurately measure

its mass! Unstable particles have uncertain mass.

2

htE

Another Uncertainty Principle

For a short enough period of time t, you can violate conservation of energy by E.

means you can measure E in time t for these times, energy conservation cannot

be violated

means you can’t measure E in time t so the universe can violate energy

conservation for shorter times and “get away with it”

E

ht

2

E

ht

2

Classically, potential energy cannot be greater than the total energy

Otherwise the kinetic energy would be negative! K = E - U

Places where U>E are classically forbidden

Tunneling

Waves can tunnel into regions where they “shouldn’t” be -- if region is small enough.

Light waves tunnel through region, even when they “should” have totally

reflected, if region is very narrow.

Matter waves tunnel through “classically forbidden regions”

Tunneling

Wait, did you say a particle can tunnel into classically forbidden region where the kinetic energy would

be negative?!!?

YUPAnother example of violating conservation of energy for short enough time - HUP

Examples of Quantum Tunneling

One type of Scanning Tunneling Microscope =

STMA small, metal needle passes very near a material.Electrons from the needle can tunnel through the small gap and into the material.The smaller the gap, the more likely the tunneling.The more tunneling happens, the stronger the current of electrons.As the needle scans across the surface

the tunneling current gives an outline of the material.

Early Atomic ModelsYou’ve learned about many physics models (theories) that are “wrong.”So far, these models have been useful.

F=ma & K=½mv2 are good when v<<c.The ray model of light is good for short wavelength.etc

WARNING:The early atomic models are not useful, except to see how we disprove theories.

Nuclear Model of Atoma tiny, massive, dense nucleus

at the center of the atomsurrounded by electrons

very little of the mass of the atom is electronsmost of the volume of the atom is electrons

OrbitsWhere are the electrons?Electrons do NOT orbit the nucleus, like planets orbit Sun

Although it seems reasonable, since the electric force and the gravitational force are very similar:

but…

2

1

rF

Two Problems with Orbits1) An orbiting electron is an accelerating charge, and

accelerating charges give off EM radiation (like an antenna),

thus giving off energy.The electron would gradually lose all its energy.That doesn’t happen -- atoms are stable.

Second Problem with Orbits

2) QuantizationA planet can be in any size orbit with any orbital energy,but electrons in atoms have only certain -- quantized -- energy levels.Orbit model can’t explain why.

Current Model of OrbitElectron “cloud” is wavefunction

describes the probability of electron being at various points around the nucleus.

Electron wave behavior based on Schroedinger equation.The electron states are quantized

3 quantum numbers for spatial state:

n, ℓ, mℓ. http://www.falstad.com/qmatom/directions.html

Principle Quantum Number

Principle quantum number, n,n = 1, 2, 3, 4, 5, ....tells what “shell” the electron is in.

n=1 is called the K-shell, n=2 is the L-shell, etc

tells a lot about the electron’s energyfor hydrogen atom, it determines the electron’s energyfor hydrogen atom:

2

eV6.13

nEn