# Mastering physics solutions half life and radioactive dating Contents:

So it has to be 18 Ar In electron capture a proton turns into a neutron. The Periodic Table is your friend. Now do a bit of work. Related Questions What happens during a nuclear reaction? Physical parameters conserved in a nuclear reaction??

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## The Basics of Nuclear Reactions ? | Yahoo Answers

Can Nuclear Fission be categorized to chemical reaction? What are the laws governing civilian nuclear reactors? How is mass lost in nuclear fusion? Answer Questions Physics question? How can I projectile vomit really far? How do I solve this physics question? What was the proof by NASA that light particle speed can be slow? Is it possible to go beyond time? Is it possible to emit darkness???? Instead of emitting light. Find in terms of and Using your result from Part E, solve for Express your answer in terms of , in terms of , , and and.

When their speeds become comparable to the speed of light , the angular frequency is no longer what you determined in Part D. Using special relativity, one can show that the angular frequency is actually given by the formula. As you can see, the frequency drops as the energy and speed increases; the particles' motion falls out of phase with the pulsating voltage, restricting the cyclotron's ability to accelerate the particles further Designing a New Particle Accelerator Description: Find the available energy for two related particle collisions.

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A new particle accelerator facility is being built. The designers are considering two designs, one using stationary targets and the other using collisions of beams with the same energy. Part A Consider a beam of protons with energy If these protons collide with stationary protons, what is the available energy in a collision? Express your answer in billions of electron volts to three significant figures. Print View with Answers 9 of 20 https: Formula for available energy Recall that the formula for available energy target particle, and is , where is the total energy of the moving particle.

What is the available energy when these beams collide? Considering the momentum In all particle collisions, momentum must be conserved. This is the reason that the available energy in collisions with a stationary target is less than the total energy of the collision: If two beams of identical protons collide head-on, what is the total momentum of a pair of protons just before the collision? What is the minimum amount of energy that must go into kinetic energy to have the same total momentum after the collision? Only the design from Part A can be chosen, because the W bosons will have low energy and will thus be easier to work with.

Only the design from Part B can be chosen, because it is the only one with enough energy to make W bosons. Either design can be chosen, because the energy of the W bosons is not a concern. Neither design can be chosen, because neither has sufficient energy to make W bosons. In this problem the student determines the quark content of particles with specific charge, baryon number, and strangeness. Assume that each particle contains only combinations of the quarks , , and and the antiquarks , , and.

Print View with Answers 10 of 20 https: Charges of quarks The electric charges of the three quarks , , and are, respectively, , where is the magnitude of the electron charge. Note that the antiquarks will have the same charge magnitude, just with opposite sign to its corresponding quark. Baryons versus mesons Recall that hadrons are a general classification of particles that consist of quarks.

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They are divided into two subclasses: Since in this problem, you are looking for a quark-antiquark pair. Definition of strangeness Strangeness is a quantum number that is used to track the number of strange particles in a hadron both mesons and baryons. If a particle has a strange quark , then it has strangeness. If the particle has an antistrange quark , then it has strangeness. These numbers are additive; two strange quarks in combination means a strangeness of.

Print View with Answers 11 of 20 https: The United States uses 1. Assume that all fission energy is converted into electrical energy.

## MasteringPhysics: Print View with Answers

Assume, that all this energy came from the fission of Assume that all fission energy is converted into electrical energy. Part A How many kilograms of would be used per year? Express your answer to two significant figures and include the appropriate units. Recall that only 0. Find the daughter nucleus of, energy released by, and number of beta and alpha decays involved in the Th decay chain.

## The Basics of Nuclear Reactions ?

When the daughter nucleus produced in a radioactive decay is itself unstable, it will eventually decay and form its own daughter nucleus. If the newly formed daughter nucleus is also unstable, another decay will occur, and the process will continue until a nonradioactive nucleus is formed. Such a series of radioactive decays is called a decay chain. A good example of a decay chain is provided by , a naturally occurring isotope of thorium. Part A The first step in the decay chain of is an alpha decay.

What is the daughter nucleus formed by this first decay?

Print View with Answers 12 of 20 https: In alpha-particle decay, a helium nucleus consisting of two protons and two neutrons is emitted from the parent atom, leaving it with four fewer nucleons and an atomic number reduced by two. Find the numbers of protons and neutrons in the daughter nucleus Recall that in radioactive decays the atomic number and mass number are conserved. How many protons and neutrons are there in the daughter nucleus when undergoes an alpha decay? Part B What is the energy The atomic mass of is How to approach the problem The energy released in a decay depends on the difference in mass, , of the system before and after the decay.

It can be calculated using the relation. You need to take into account the mass of the particle emitted in the decay when calculating the mass of the system after the decay. Also, note that the number of electrons in the parent nucleus is the same as the number of electrons in the daughter nucleus plus the number of electrons in the alpha particle, so the electrons do not contribute to the total mass difference. Find the mass difference What is the difference in mass, , of the system before and after the alpha decay?

Express your answer numerically in atomic mass units to four significant digits. Atomic mass of an alpha particle The atomic mass of an alpha particle is 4. Print View with Answers 13 of 20 https: Beta decay In a beta-minus decay, an electron as well as an antineutrino with negligible mass is emitted as a neutron is converted into a proton. Such a decay increases the atomic number by one without changing the number of nucleons.

How many alpha decays will occur during this chain process? Alpha decay In alpha-particle decay, a helium nucleus consisting of two protons and two neutrons is emitted from the parent atom, leaving it with four fewer nucleons and an atomic number reduced by two. The equations for decay and half-life are derived, and then a simple problem in carbon dating is solved. To understand decay in terms of half-life and to solve radioactive dating problems.

Particles in a nucleus are bound by the strong force. A reasonable model of this binding would be a barrier potential of finite energy. Quantum mechanics allows a small, nonzero probability for a particle to "tunnel" through a potential barrier. Working with this rough model, we can say that, for a given unstable nucleus, there is a constant probability of some particle, say an alpha particle, tunneling through the barrier and being emitted as radiation.

Since this probability is constant, depending only on the particular nuclide involved, you would expect the number of decays per second to be proportional to the number of nuclei present. Since the number of decays is the same as the amount by which the total number of nuclei of the particular type being considered is reduced, you can construct the relationship , where is the number of nuclei at a time. The constant of proportionality is called the decay constant.

Part A If , where is some constant, what is Express your answer in terms of?

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• Thus, is the general solution to the differential equation for radioactive decay. Part B Given that at time there is a quantity of nuclei present Express your answer in terms of in other words, , find the value of the constant in the equation. Print View with Answers 14 of 20 Since https: Find the time at which half of the original number of nuclei will remain. What values to use Which of the following correctly pairs the value of and the value of that should be entered into to find the value of?

The number is called the half-life of the nucleus. Frequently, the half-life is given instead of the decay constant when discussing the decay of radioactive nuclei. If you measure the number of nuclei at any time and then wait one half-life, of the nuclei will remain. If you wait two half-lives then will remain.

If you wait three half-lives, will remain, and so on. The decay of radioactive nuclei can be used to measure the age of artifacts, fossils, and rocks. Dating an organic artifact entails looking at its carbon content. Carbon exists in three isotopic forms: Both and are stable whereas is radioactive. To find the age of an organic artifact, first, you measure how much is found within the artifact.

Then, you estimate how much would have been in it when it was first made. You then plug these two values into the decay equation to find how old the artifact is. The quantity of originally in the artifact may be estimated fairly accurately because the percent of atmospheric carbon in the form of the isotope stays relatively constant with time. Since plants constantly take in new carbon from atmospheric carbon dioxide, the percent of in a plant should be the same as the percent in the atmosphere, until the plant dies and stops taking in new carbon.

Therefore, you can use this percent and the present quantity of total carbon in the artifact to find how much was in it when it died. The half-life of is years. Print View with Answers 15 of 20 https: If a sample shows only one-fourth of its estimated original quantity of need to plug into it at all for this problem. Think about half-lives; don't try to just plug into the decay equation. You shouldn't Express your answer in years to three significant figures. Express your answer as an integer.

To solve more general carbon dating problems, you must first find the value of the decay constant for Using the given half-life, years, find the value of the decay constant for. Most problems are not , so that you can easily use the decay equation. Express your answer in inverse years to three significant figures. Relating and Recall that in Part C you found the relation. How old is the cloth?

Express your answer in years to two significant figures. Radioactive dating is an important technique used by archaeologists to find the age of newly discovered items and to determine the authenticity of supposed artifacts. Food is often irradiated with either x rays or electron beams to help prevent spoilage. A low dose of kilorads krad helps to reduce and kill inactive parasites, a medium dose of krad kills microorganisms and pathogens such as A low dose of kilorads dose of kills microorganisms and pathogens such as salmonella, and a high dose of refrigeration. If x rays are used, what would be the dose in? Print View with Answers 16 of 20 https: Part B What would be the dose in? The isotope undergoes decay with a half-life of Print View with Answers 17 of 20 https: Part A What is the activity of 1.

The isotope undergoes decay with a half-life of 28 years. Part A What nucleus is produced by this decay?

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Part B If a nuclear power plant is contaminated with Sr, how long will it take for the radiation level to decrease to 1. Express your answer using two significant figures. Radioactive isotopes used in cancer therapy have a "shelf-life," just like pharmaceuticals used in chemotherapy. When its activity falls below Just after it has been manufactured in a nuclear reactor, the activity of a sample of is When its activity falls below , it is considered to be too weak a source to use in treatment. You work in the radiology department of a large hospital. One of these sources in your inventory was manufactured on October 6, It is now April 6, Part A Is the source still usable?

The half-life of is 5. It has become popular for some people to have yearly whole-body scans CT scans, formerly called CAT scans , using x rays, just to see if they detect anything suspicious. A number of medical people have recently questioned the advisability of such