H P180B Comprehensive Final
Fall 2005
Be prepared to answer 4 of the six questions/problems below
2 hours 150 points
Extra Credit answer a fifth question!
You can have one 3 x 5 index card of information
  Electricity and Magnetism (ElectroMagnetism)
1) Mass Spectrometry

Radiocarbon Dating
using Accelerator Mass Spectrometry (AMS) differs from the decay counting methods in that the amount of C-14 in the sample is measured directly, rather than by waiting for the individual radioactive decay events to occur. This makes the technique 1,000 to 10,000 times more sensitive than decay counting.

The enhanced sensitivity is achieved by accelerating sample atoms as ions to high energies using a particle accelerator, and using nuclear particle detection techniques.

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University of Arizona

1) One form of mass spectrometer accelerates ions by a voltage V before they enter a magnetic field B. The ions are assumed to start from rest. Show that the mass of an ion is m = q(BR)^2/2V, where R is the radius of the ions’ path in the magnetic field and q is their charge. [Problem #64 Chapter 20].

2) Draw a diagram of a mass spectrometer. Include the source where the sample is ionized, the velocity selector and the detection apparatus

3) Describe the physics involved with separating a sample into its constituent particles. Explain the mathematical equations that are associated with the physics.

4) Explain how would a scientist use the mass spectrometer to find the date something? Utilize an example from the list below.

ANSTO: Archaeology, Bomb Pulse, Grenhouse Gases, Historical
2) The Action Potential

The Action Potential
In response to the appropriate stimulus, the cell membrane of a nerve cell goes through a sequence of depolarization from its rest state followed by repolarization to that rest state. In the sequence, it actually reverses its normal polarity for a brief period before reestablishing the rest potential.

The action potential sequence is essential for neural communication. The simplest action in response to thought requires many such action potentials for its communication and performance.

For modeling the action potential for a human nerve cell, a nominal rest potential of -70 mV will be used. The process involves several steps.

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1) Capacitance of an Axon. a) Do an order-of-magnitude estimate for the capacitance of an axon 10 cm long of radius 10 micrometers. The thickness of the membrane is about 10^-8 m, and the dielectric constant is about 3. B) By what factor does the concentration (number of ions per volume) of Na+ ions in the cell change as a result of one action potential? [Example 18-15 Chapter 18].

2) Draw a diagram of an axon and the action potential graph. Explain the different regions of the graph.

3) Describe the physics involved with the flow of electric charge in the axon. Explain the mathematical equations that are associated with the physics.

Action Potential: 1, 2, 3

Light and Optics
3) Interference Microscope

An Intereference Microscope
makes use of wave properties of light in a direct way to increase contrast in a transparent object.

In the mid-1950s, a French optics theoretician named Georges Nomarski modified the Wollaston prism used for detecting optical gradients in specimens and converting them into intensity differences. Today there are several implementations of this design, which are collectively called differential interference contrast (DIC).

Living or stained specimens, which often yield poor images when viewed in brightfield illumination, are made clearly visible by optical rather than chemical means.

Molecular Expressions

Constructive Interference occurs when the path difference equals a whole number of wavelengths.
Destructive Intereference occurs when the path difference is 1/2 or 3/2 wavelengths.

1) What optics principles are utilized in the Interference Microscope?
2) Draw a diagram of the Constructive and Destructive interference conditions.
3) What are the advantages of an Interference Microscope?

Interference Microscope 1, 2

4) Global Positioning System (Relativity)

Finding Nemo

When people talk about "a GPS," they usually mean a GPS receiver. The Global Positioning System (GPS) is actually a constellation of 27 Earth-orbiting satellites (24 in operation and three extras in case one fails). The U.S. military developed and implemented this satellite network as a military navigation system, but soon opened it up to everybody else.

Each of these 3,000- to 4,000-pound solar-powered satellites circles the globe at about 12,000 miles (19,300 km), making two complete rotations every day. The orbits are arranged so that at any time, anywhere on Earth, there are at least four satellites "visible" in the sky.

How Stuff Works

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1) A relativity correction to GPS. GPS satellites move at about 4 km/s = 4000 m/s. Show that a good GPS receiver needs to correct for time dilation if it is to produce results consistent with atomic clocks accurate to
1 part in 10 trillion.[Conceptual Example 26-4]
2) Explain the physical concept of Special Relativity and Time Dilation. According to Van Flandern, why are GR and SR important in GPS?
3) Draw a diagram of time dilation. Explain why the conceptis mathematically a simple idea. [Remember?]

General Relativity (GR) predicts that clocks in a stronger gravitational field will tick at a slower rate. Special Relativity (SR) predicts that moving clocks will appear to tick slower than non-moving ones. Remarkably, these two effects cancel each other for clocks located at sea level anywhere on Earth.
Tom Van Flandern, Univ. of Maryland & Meta Research

Global Positioning System 1, 2

Modern Physics

5) The emergence of Quantum Philosophy

      In Quantum Theory, all events are possible (because the initial state of the system is indeterminate), but some are more likely than others. While the quantum physicist can say very little about the likelihood of any single event's happening, quantum physics works as a science that can make predictions because patterns of probability emerge in large numbers of events. It is more likely that some events will happen than others, and over an average of many events, a given pattern of outcome is predictable. Thus, to make their science work for them, quantum physicists assign a probability to each of the possibilities represented in the wave function.Quantum Mechanics divides the world into two parts, commonly called the [system and the observer]. Except at specified times the system and the observer do not interact. An interaction at those specified times is called a measurement. Quantum Mechanics predicts all the information that the observer can possibly obtain about the system. This information can be represented in different ways. It is often represented in terms of a wave function. A measurement changes the information an observer has about the system and therefore changes the wave function of the system.

1) What three experiments led to the collapse of Classical (Newtonian) Theory?
2) Draw diagrams of each experiment and explain the physical principle that shot down Newton's deterministic philosophy of nature.
3) What is Entanglement? How is this concept changing the way we view the universe?

"I was born not knowing and have had only a little time to change that here and there."
Richard Feynman
PhotoElectric Effect
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Quantum Theory 1, 2, 3

6) Big Bang Cosmology
The Big Bang

The Big Bang Model is a broadly accepted theory for the origin and evolution of our universe. It postulates that 12 to 14 billion years ago, the portion of the universe we can see today was only a few millimeters across. It has since expanded from this hot dense state into the vast and much cooler cosmos we currently inhabit. We can see remnants of this hot dense matter as the now very cold cosmic microwave background radiation which still pervades the universe and is visible to microwave detectors as a uniform glow across the entire sky.

1) What are the pillars (Evidence) of the Big Bang Theory? Why do we call it a theory and not a hypothesis?
2) Our Sun rotates about the center of the galaxy at a distance of 30,000 light years. The Solar system revolves around the galaxy at 250 km/s. How massive is the Milky Way Galaxy? Use Kepler's Third Law. An example.

Cosmic Microwave Background

. . .a baby picture of the universe!
  Big Bang Cosmology 1, 2, 3, 4