Archive for May, 2012

The Standard Model of Particle Physics

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Assignments

EQ: What is matter and energy?

Agenda

Matter and Antimatter

As we’ve learned previously, the atom is the smallest part of an element (such as oxygen) that has the characteristics of the element. Atoms are made up of very small negatively charged electrons surrounding, surrounding the much larger nucleus. The nucleus is composed of positively charged protons and neutral neutrons. The positively charged protons exert a repelling electrical force upon each other, but the strong nuclear force holds the protons and neutrons together in the nucleus.

This completely summarized our understanding of atomic structure until the 1930s, when scientists began to discover evidence that there was more to the picture, and that protons and nucleons were made up of even smaller particles. This launched the particle physics movement, which, to this day, continues to challenge our understanding of the entire universe by exploring the structure of the atom.

In addition to matter we’re familiar with, researchers have discovered the existence of antimatter. Antimatter is matter made up of particles with the same mass as regular matter particles, but opposite charges and other characteristics. An antiproton is a particle with the same mass as a proton, but a negative (opposite) charge. A positron has the same mass as an electron, but a positive charge. An antineutron has the same mass as a neutron, but has other characteristics opposite that of the neutron.

When a matter particle and its corresponding antimatter particle meet, the particles may combine to annihilate each other, resulting in the complete conversion of both particles into energy consistent with the mass-energy equivalence equation: E=mc2.

Question: A proton and an antiproton collide and completely annihilate each other. How much energy is released? (mproton=1.67*10-27kg)

Forces in the Universe

We’ve dealt with many types of forces in this course, ranging from contact forces such as tensions and normal forces to field forces such as the electrical force and gravitational force. When observed from their most basic aspects, however, we can consolidate all observed forces in the universe into the following four known fundamental forces. They are, from strongest to weakest:

1. Strong Nuclear Force: holds protons and neutrons together in the nucleus
2. Electromagnetic Force: electrical and magnetic attraction and repulsion
3. Weak Force: responsible for radioactive beta decay
4. Gravitational Force: attractive force between objects with mass

Understanding these forces remains a topic of scientific research, with current work exploring the possibility that forces are actually conveyed by an exchange of force-carrying particles such as photons, bosons, gluons, and gravitons.

Classification of Matter

The current model of sub-atomic structure used to understand matter is known as the Standard Model. Development of this model began in the late 1960s, and has continued through today with contributions from many scientists across the world. The Standard Model explains the interactions of the strong (nuclear), electromagnetic, and weak forces, but has yet to account for the gravitational force. The search for the theorized Higgs Boson at Fermilab and CERN is an attempt to better unify and strengthen the Standard Model.

Although the Standard Model itself is a very complicated theory, the basic structure of the model is fairly straightforward. According to the model, all matter is divided into two categories, known as hadrons and the much smaller leptons. All of the fundamental forces act on hadrons, which include particles such as protons and neutrons. In contrast, the strong nuclear forces doesn’t act on leptons, so only three fundamental forces act on leptons such as electrons, positrons, muons, tau particles and neutrinos.

Hadrons are further divided into baryons and mesons. Baryons such as protons and neutrons are composed of three smaller particles known as quarks. Charges of baryons are always whole numbers. Mesons are composed of a quark and an anti-quark (for example, an up quark and an anti-down quark).

Quarks and Leptons

Scientists have identified six types of quarks. For each of the six types of quarks, there also exists a corresponding anti-quark with an opposite charge. The quarks have rather interesting names: up quark, down quark, charm quark, strange quark, top quark, and bottom quark. Charges on each quark are either one third of an elementary charge, or two third of an elementary charge, positive or negative, and the quarks are symbolized by their first letter. For the associated anti-quark, the symbol is the first letter of the anti-quark’s name, with a line over the name. For example, the symbol for the up quark is u. The symbol for the anti-up quark is .

Similarly, scientists have identified six types of leptons: the electron, the muon, the tau particle, and the electron neutrino, muon neutrino, and tau neutrino. Again, for each of these leptons there also exists an associated anti-lepton. The most familiar lepton, the electron, has a charge of -1e. Its anti-particle, the positive, has a charge of +1e.

Since a proton is made up of three quarks, and has a positive charge, the sum of the charges on its constituent quarks must be equal to one elementary charge. A proton is actually comprised of two up quarks and one down quark. If we verify this by adding up the charges of the proton’s constituent quarks (uud):

Question: A neutron is composed of up and down quarks. How many of each type of quark are needed to make a neutron?

Answer: The charge on the neutron must sum to zero, and the neutron is a baryon, so it is made up of three quarks. To achieve a total charge of zero, the neutron must be made up of one up quark (+2/3e) and two down quarks (-1/3e).

If the charge on a quark (such as the up quark) is +2/3e, the charge of the anti-quark () is -2/3e. The anti-quark is the same type of particle, with the same mass, but with the opposite charge.

Question: What is the charge of the down anti-quark ()?

Answer: The down quark’s charge is -1/3e, so the anti-down quark’s charge must be +1/3e.

Question: Compared to the mass and charge of a proton, an antiproton has

1. the same mass and the same charge
2. greater mass and the same charge
3. the same mass and the opposite charge
4. greater mass and the opposite charge

Answer: (3) the same mass and the opposite charge

Mass-Energy Equivalence

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In 1905, in a paper titled "Does the Inertia of a Body Depend Upon Its Energy Content," Albert Einstein proposed the revolutionary concept that an object’s mass is a measure of how much energy that object contains, opening a door to a host of world-changing developments, eventually leading us to the major understanding that the source of all energy in the universe is, ultimately, the conversion of mass into energy!

Conservation Laws

If mass is a measure of an object’s energy, we need to re-evaluate our statements of the law of conservation of mass and the law of conservation of energy. Up to this point, we have thought of these as separate statements of fact in the universe. Based on Einstein’s discovery, however, mass and energy are two concepts effectively describing the same thing, therefore we could more appropriately combine these two laws into a single law, the law of conservation of mass-energy, which states that mass-energy cannot be created nor destroyed.

The concept of mass-energy is one that is often misunderstood and oftentimes argued in terms of semantics… for example, a popular argument states that the concept of mass-energy equivalence means that mass can be converted to energy, and energy can be converted to mass. Many would disagree that this can occur, countering that since mass and energy are effectively the same thing, you can’t convert one to the other. For our purposes, we’ll save these arguments for future courses of study, and instead focus on a basic conceptual understanding.

The universal conservation laws we have studied so far this course include:

• Conservation of Mass-Energy
• Conservation of Charge
• Conservation of Momentum

E=mc2

Einstein’s famous formula, E=mc2, relates the amount of energy contained in matter to the mass times the speed of light in a vacuum (c=3*108 m/s) squared. Theoretically, then, we could determine the amount of energy represented by 1 kilogram of matter as follows:

Question: What is the energy equivalent of 1 kilogram of matter?

This is a very large amount of energy… to put it in perspective, the energy equivalent of a large pickup truck is in the same order of magnitude of the total annual energy consumption of the United States!

More practically, however, it is not realistic to convert large quantities of mass completely into energy. Current practice revolves around converting small amounts of mass into energy in nuclear processes. Typically these masses are so small that measuring in units of kilograms isn’t practical. Instead, scientists often work with the much smaller universal mass unit (u), which is equal in mass to one-twelfth the mass of a single atom of Carbon-12. The mass of a proton and neutron, therefore, is close to 1u, and the mass of an electron is close to 5*10-4u. In precise terms, 1u=1.66053886*10-27kg.

One universal mass unit (1u) completely converted to energy is equivalent to 931 MeV. Because mass and energy are different forms of the same thing, this could even be considered a unit conversion problem. If given a mass in universal mass units, you can use this equivalence directly from the front of the Regents Physics Reference Table to solve for the equivalent amount of energy, without having to convert into standard units and utilize the E=mc2 equation.

Question: If a deuterium nucleus has a mass of 1.53*10-3 universal mass units (u) less than its components, how much energy does its mass represent?

Binding Energy

The nucleus of an atom consists of positively charged protons and neutral neutrons. Collectively, these nuclear particles are known as nucleons. Protons repel each other electrically, so why doesn’t the nucleus fly apart? There is another force which holds nucleons together, known as the strong nuclear force. This extremely strong force overcomes the electrical repulsion of the protons, but it is only effective over very small distances.

Because nucleons are held together by the strong nuclear force, you must add energy to the system to break apart the nucleus. The energy required to break apart the nucleus is known as the binding energy of the nucleus.

If measured carefully, we find that the mass of a stable nucleus is actually slightly less than the mass of its indivudal component nucleons. The difference in mass between the entire nucleus and the sum of its component parts is known as the mass defect (m). The binding energy of the nucleus, therefore, must be the energy equivalent of the mass defect due to the law of conservation of mass-energy: .

Fission & Fusion

Fission is the process in which a nucleus splits into two or more nuclei. For heavy (larger) nuclei such as Uranium-235, the mass of the original nucleus is greater than the sum of the mass of the fission products. Where did this mass go? It is released as energy! A commonly used fission reaction involves shooting a neutron at an atom of Uranium-235, which briefly becomes Uranium-236, an unstable isotope. The Uranium-236 atom then fissions into a Barium-141 atom and a Krypton-92 atom, releasing its excess energy while also sending out three more neutrons to continue a chain reaction! This process is responsible for our nuclear power plants, and is also the basis (in an uncontrolled reaction) of atomic fission bombs.

Fusion, on the other hand, is the process of combining two or more smaller nuclei into a larger nucleus. If this occurs with small nuclei, the product of the reaction may have a smaller mass its precursors, thereby releasing energy as part of the reaction. This is the basic nuclear reaction that fuels our sun and the stars as hydrogen atoms combine to form helium. This is also the basis of atomic hydrogen bombs.

Nuclear fusion holds tremendous potential as a clean source of power with widely available source material (we can create hydrogen from water). The most promising fusion reaction for controlled energy production fuses two isotopes of hydrogen known as deuterium and tritium to form a helium nucleus and a neutron, as well as an extra neutron, while releasing a considerable amount of energy. Currently, creating a sustainable, controlled fusion reaction that outputs more energy than is required to start the reaction has not yet been demonstrated, but remains an area of focus for scientists and engineers.

Regents Physics Exam Prep Resources #physicsed #regents #physics

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As we close in on the end of our year in high school physics, I thought it’d be helpful to myself (and perhaps to others) to put together a compendium of some of the best Regents/Honors Physics resources to assist students in preparing for their final exams.  Without further ado, and in no particular order:

APlusPhysics: Dan Fullerton’s (my) site to assist students and educators specifically around the NY Regents Physics curriculum, which has been expanding and generalizing to curricula outside the state as well.  The Regents Physics section of the site, however, is by far the strongest and most complete.  This site includes online tutorials covering the entire Regents Physics course, interactive quizzes pulling from a database of hundreds of old Regents Physics Exam questions, video tutorials of every major topic covered by the exam, and is also tied in quite closely with the Regents Physics Essentials review book.  In addition, every Regents Physics questions from the past 16 exams has been pulled into worksheets by topic to allow for highly directed practice.

ScienceWithMrNoon: Brendan Noon‘s physics site has a wide variety of great content, including topic-based interactive quizzes and tons of great physics videos.  His course calendar, as well, is loaded with tons of great resources by topic!

St. Mary’s Physics: Tony Mangiacapre‘s site, full of great lessons and interactive simulations across the entire Regents Physics curriculum.  I’m especially fond of the Photoelectric Effect simulation — makes for a great computer-based lab activity!  This site is also closely linked with Tony’s 123physics.com, featuring more than 1300 Regents Physics Exam questions broken down by topic for students to practice, as well as more great videos.

RegentsPrep.org: The Oswego City School District (with Dr. Tom Altman) has pulled together a strong collection of resources broken into Explanations, Demos, Labs, and Quizzes to assist students and educators in preparing for the Regents Physics exam.

Altman Science: The charismatic Dr. Tom Altman provides real-life demonstrations and explanations of physics concepts in action as part of the High School Physics Project.  Further, he’s broken down a number of old Regents Exams and walked through solutions to each and every question in video format, page by page.  In addition, his laser videos are “wicked cool” as well!

Past Regents Exams: The name says it all — an amazing archive of old Regents Physics exams!

Regents Physics Essentials: I’d feel negligent if I didn’t point out the Regents Physics Essentials review book I put together at student urging a few years back.  There are a number of great review books to help students get ready for the exam, but this book takes a slightly different twist by providing students a straightforward, clear explanation of the fundamental concepts and more than 500 sample questions with fully-worked out solutions directly integrated in the text.  As stated by my physics teaching cohort in crime at our high school, “the best review book is the one students will actually use,” and this was written to be friendly, fun, and concise.  Plus, if students/teachers want extra problems without solutions given, the worksheets are available free online!  You can check out the book’s free preview on APlusPhysics or use Amazon’s “Look Inside” feature!

Atomic Spectra

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Once you understand the energy level diagram, it quickly becomes obvious that atoms can only emit certain frequencies of photons, correlating to the difference between energy levels as an electron falls from a higher energy state to a lower energy state. In similar fashion, electrons can only absorb photons with energy equal to the difference in energy levels as the electron jumps from a lower to a higher energy state. This leads to unique atomic spectra of emitted radiation for each element.

An object that is heated to the point where it glows (incandescence) emits a continuous energy spectrum, described as blackbody radiation.

If a gas-discharge lamp is made from mercury vapor, the mercury vapor is made to emit light by application of a high electrical potential. The light emitted by the mercury vapor is created by electrons in higher energy states falling to lower energy states, therefore the photons emitted correspond directly in wavelength to the difference in energy levels of the electrons. This creates a unique spectrum of frequencies which can be observed by separating the colors using a prism, known as an emission spectrum. By analyzing the emission spectra of various objects, scientists can determine the composition of those objects.

In similar fashion, if light of all colors is shone through a cold gas, the gas will only absorb the frequencies corresponding to photon energies exactly equal to the difference between the gas’s atomic energy levels. This creates a spectrum with all colors except those absorbed by the gas, known as an absorption spectrum.

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