CK-12 People's Physics Book Version 2

by James H. Dann

  Example:

  Radioactivity and Nuclear Physics Problem Set

  After seconds, the mass of a sample of radioactive material has reduced from grams to grams. Its half-life must be

  Which of the following is true for the following reaction?

  This is a fission reaction.

  This is a fusion reaction.

  This is not a valid reaction, because the equations don’t balance.

  For any radioactive material, its half-life… …first decreases and then increases.

  …first increases and then decreases.

  …increases with time.

  …decreases with time.

  …stays the same.

  If the half-life of a substance is seconds, it ceases to be radioactive (i.e. it ceases emitting particles), … … after seconds.

  … after seconds

  … after seconds.

  … after a very long time.

  You detect a high number of alpha particles every second when standing a certain distance from a radioactive material. If you triple your distance from the source, the number of alpha particles you detect will decrease. By what factor will it decrease?

  It will stay the same.

  You have grams of radioactive substance A and grams of radioactive substance B. Both decay by emitting alpha-radiation, and you know that the higher the number of alpha-particles emitted in a given amount of time, the more dangerous the sample is. Substance A has a short half-life (around days or so) and substance B has a longer half-life (around months or so). Which substance is more dangerous right now? Explain.

  Which substance will be more dangerous in two years? Explain.

  Write the nuclear equations for the following reactions. The alpha decay of .

  The beta decay of .

  The beta decay of .

  The alpha decay of .

  A certain radioactive material has a half-life of minutes. Suppose you have a large sample of this material, containing atoms. How many atoms decay in the first minutes?

  Does this strike you as a dangerous release of radiation? Explain.

  How many atoms decay in the second minutes?

  What is the ratio of the number of atoms that decay in the first minutes to the number of atoms that decay in the second minutes?

  How long would you have to wait until the decay rate drops to % of its value in the first 8 minutes?

  There are two equal amounts of radioactive material. One has a short half-life and the other has a very long half-life. If you measured the decay rates coming from each sample, which would you expect to have a higher decay rate? Why?

  Hidden in your devious secret laboratory are grams of radioactive substance A and grams of radioactive substance B. Both emit alpha-radiation. Quick tests determine that substance A has a half-life of days and substance B has a half-life of days. How many grams of substance A and how many grams of substance B will you have after waiting days?

  Which sample (A or B) is more dangerous at this point (i.e., after the days have passed)?

  The half-life of a certain radioactive material is years. After years, how much of a g sample of this material will remain?

  The half life of is seconds. You begin with of . How much is left after seconds?

  You want to determine the half-life of a radioactive substance. At the moment you start your stopwatch, the radioactive substance has a mass of . After minutes, the radioactive substance has grams left. What is its half-life?

  The half-life of is years. You have micrograms left, and the sample you are studying started with micrograms. How long has this rock been decaying?

  A certain fossilized plant is years old. Anthropologist Hwi Kim determines that when the plant died, it contained of radioactive . How much should be left now?

  Jaya unearths a guinea pig skeleton from the backyard. She runs a few tests and determines that % of the original is still present in the guinea pig’s bones. The half-life of is years. When did the guinea pig die?

  You use the carbon dating technique to determine the age of an old skeleton you found in the woods. From the total mass of the skeleton and the knowledge of its molecular makeup you determine that the amount of it began with was grams. After some hard work, you measure the current amount of in the skeleton to be grams. How old is this skeleton? Are you famous?

  Micol had in her lab two samples of radioactive isotopes: with a half-life of days and with a half-life of days. She initially had of the former and of the latter. Do a graph of quantity remaining (vertical axis) vs. time for both isotopes on the same graph.

  Using the graph determine at what time the quantities remaining of both isotopes are exactly equal and what that quantity is.

  Micol can detect no quantities less than . Again, using the graph, determine how long she will wait until each of the original isotopes will become undetectable.

  The goes through decay and the decays by means of electron capture. What are the two immediate products of the radioactivity?

  It turns out both of these products are themselves radioactive; the product goes through decay before it becomes stable and the product goes through decay before it reaches a stable isotope. When all is said and done, what will Micol have left in her lab?

  Answers to Selected Problems

  .

  .

  .

  .

  .

  a. Substance decays faster than b. Substance because there is more material left to decay.

  a. b.

  c.

  d.

  a. atoms b. Decay of a lot of atoms in a short period of time

  c. atoms

  d.

  e. minutes

  The one with the short half life, because half life is the rate of decay.

  a. Substance and substance b. substance

  minutes

  years

  years

  years

  Chapter 26: Standard Model of Particle Physics Version 2

  The Big Idea

  All matter is composed of fundamental building blocks, called the elementary particles. These building blocks are much smaller than an atom, and so are sometimes referred to as subatomic particles. Particles interact with one another according to a set of laws. There are two types of particles: force particles (fermions) and matter particles (bosons). What sets them apart is an intrinsic property called 'spin'. The set of particles and the laws that govern their interactions are called the Standard Model. The Standard Model is very powerful and can predict particle interactions to amazing accuracy.

  The fifth of the five conservation laws is called CPT symmetry. CPT is a symmetry between matter and anti-matter. The law states that if you reverse the spatial coordinates of a particle, change it from matter to anti-matter, and reverse it in time the new object is now indistinguishable from the original. More on the fifth conservation law in the Feynman Diagram's chapter.

  Matter

  Particles can be grouped into two camps: fermions and bosons. Typically matter is made up of fermions, while interactions (which lead to forces of nature such as gravity and electromagnetism) occur through the exchange of particles called bosons. (There are exceptions to this.) Electrons and protons are fermions, while photons (light particles) are bosons.

  Fermions (matter particles) can be broken into two groups: leptons and quarks. Each of these groups comes in three families.

  The first family of leptons consists of the electron and the electron neutrino. The second family consists of the muon and the muon neutrino. The third consists of the tau and the tau neutrino. Particles in each successive family are more massive than the family before it.

  The first family of quarks consists of the up and down quark. The second family consists of the charm and strange quarks. The third family consists of the top and bottom quarks.

  Up and down quarks combine (via the strong force) to form nucleons. Two ups and a down quark make a proton, while an up quark and two down quarks make a neutron. Dif
ferent combinations of quarks are called mesons. In reality, most of the mass of a proton, neutron, etc. is made up of binding energy and virtual particles.

  Particles differ in their mass, their electric charge, their family (in the case of leptons), and their “spin.” Spin is a quantum mechanical concept that is best explained as a magnetic moment intrinsic to the particle and manifested as angular momentum.

  Interactions

  There are four fundamental forces in nature. From weakest to strongest, these are the gravitational force, the weak nuclear force, the electromagnetic force, and the strong nuclear force.

  Each fundamental force is transmitted by its own boson(s): for gravity, they are called gravitons; for the weak nuclear force, they are called bosons; for the electromagnetic force, they are called photons; and for the strong nuclear force, they are called gluons.

  In summary, the building blocks of matter and the interactions between matter consist of the following fundamental particles :

  Fermions Fermions

  Leptons Quarks

  electron up

  electron neutrino down

  muon strange

  muon neutrino charm

  tau top

  tau neutrino bottom

  Bosons Bosons

  Force Transmitted Associated Boson

  gravity graviton

  electromagnetic photon

  weak

  strong gluons

  Rules

  For any interaction between particles, the five conservation laws (energy, momentum, angular momentum, charge, and CPT) must be followed. For instance, the total electric charge must always be the same before and after an interaction.

  Electron lepton number is conserved. This means that the total number of electrons plus electron neutrinos must be the same before and after an interaction. Similarly, muon lepton number and tau lepton number are also (separately) conserved. Note that matter gets lepton number of and antimatter has lepton number of .

  Total quark number is conserved. Unlike leptons, however, this total includes all families. Again matter particles get quark number of and antimatter .

  Photons can only interact with objects that have electric charge. This means that particles without charge (such as the electron neutrino) can never interact with photons.

  The strong nuclear force can only act on quarks. This means that gluons (the particle that carries the strong nuclear force) can only interact with quarks, or other gluons.

  The gravitational force can only act on objects with energy, and hence any object with mass.

  The weak nuclear force interacts with both quarks and leptons. However, the weak force is carried by any of three particles, called intermediate vector bosons: . Note that the W particles carry electric charge. This means you have to be more careful in making sure that any weak force interaction conserves electric charge.

  Any interaction which obeys all of these rules, and also obeys the usual rules of energy and momentum conservation, is allowed. Due to the randomness of particle interactions, any allowed interaction must eventually happen and thus has a non-zero probability of happening.

  Antimatter

  In addition to all of this, there is a further complication: each type of particle that exists (such as an electron or an up quark) has an antiparticle. Antiparticles are strange beasts: they have the same properties as their corresponding particles (mass, size, interactions) but their quantum numbers are exactly reversed electric charge, electron, muon, or tau lepton number, and quark number).

  There are two ways to denote something as an antiparticle. The most common is to draw a horizontal line above the thing. So, for instance, the antiparticle of the up quark is the anti-up quark:

  For charged leptons, you can merely switch the charge. So, for instance, an electron has negative charge and is written , while its antiparticle, the anti-electron (also called a positron) is written .

  Particles and antiparticles annihilate each other, and convert their mass directly to energy in the form of gamma rays. Likewise, gamma rays can spontaneously revert to particle-antiparticle pairs. Matter and energy exchange places frequently in this process, with a conversion formula given by the famous equation .

  Resources

  Ask your teacher to provide you with a copy of the Standard Model of Particles and Interactions. If there aren’t any available, please download and print out a copy of the Standard Model of Particles and Interactions, available at http://particleadventure.org/

  Standard Model of Particle Physics Problem Set

  You will need a copy of the Standard Model to do this assignment. See above.

  Which is more massive, the strange quark or the muon?

  If you bound an up quark to an anti-strange quark using gluons, would the result be a proton, a neutron, an electron, or some type of meson?

  Name three particles that do not interact with gluons.

  Name three particles that do not interact with photons.

  Which nucleon does not interact with photons? Why?

  Does the electron neutrino interact with photons? Why or why not?

  What quarks make up an anti-proton?

  What rule would be violated if Dr. Shapiro attempted to turn an anti-electron (positron) into a proton?

  Can any of the intermediate vector bosons () interact with light? If so, which?

  What force (of the four) must be involved in the process of beta decay, in which a neutron disappears and turns into a proton, an electron, and an electron anti-neutrino?

  In the world-view provided by the Standard Model, the universe of the very small contains which of the following? (Choose any and all that apply.) Boson-exchange interactions between different types of quarks and leptons

  Annihilation and creation of particle-antiparticle pairs

  Electromagnetic interactions between charged objects

  Electromagnetic interactions between bosons

  Weak interactions involving quarks and leptons

  f. Strong interactions between water molecules Explain.

  What is string theory? Why isn’t string theory mentioned anywhere on the Standard Model? (If you are not already familiar with string theory, you may have to do some research online.)

  Name three winners of the Nobel Prize who were directly investigating atomic and subatomic particles and interactions. Investigate online.

  Answers to Selected Problems

  strange

  some type of meson

  Electron, photon, tau

  Neutron, electron neutrino,

  Neutron, because it doesn’t have electrical charge

  No, because it doesn’t have electrical charge

  Two anti-up quarks and an anti-down quark

  Lepton number, and energy/mass conservation

  Yes, , because they both have charge

  The weak force because it can interact with both quarks and leptons

  Yes; a,b,c,e; no; d,f

  The standard model makes verifiable predictions, string theory makes few verifiable predictions.

  Chapter 27: Feynman Diagrams Version 2

  The Big Idea

  The interaction of subatomic particles through the four fundamental forces is the basic foundation of all the physics we have studied so far. There’s a relatively simple way to calculate the probability of collisions, annihilations, or decays of particles, invented by physicist Richard Feynman, called Feynman diagrams. Drawing Feynman diagrams is the first step in visualizing and predicting the subatomic world. If a process does not violate a known conservation law, then that process must exist with some probability. All the Standard Model rules of the previous chapter are used here. You are now entering the exciting world of particle physics.

  Key Concepts

  To make a Feynman diagram, you plot time on the horizontal axis and position on the vertical axis. This is called a space-time diagram.

  The fifth conservation law: CPT symmetry. States that if you charge conjugate (i.e. change ma
tter to anti-matter), Parity reversal (i.e. mirror reflection) and then reverse the flow of time, a matter particle is exactly the same as the anti-matter particle (see below)

  This is why anti-matter has its time arrow pointing backwards. And on collision diagrams, the matter is identical to the anti-matter after a CPT operation.

  If a particle is not moving, then we say that its space coordinate is fixed. Of course, if it’s just sitting there, then it’s moving through time. On the diagram below (left), the horizontal line shows the path of motion of a stationary particle. The diagram to the right shows the path of motion of a particle moving away from the origin at some speed.

  Here are two particles colliding! Watch out!

  We use the following symbols in Feynman diagrams:

  Annihilation Diagram: When matter and antimatter particles collide, they annihilate, leaving behind pure energy for the example below in the form of electromagnetic radiation (photons!). A different set of matter and antimatter is recreated soon thereafter. The Feynman diagram for that process looks like this: