# Half life and radioactive dating mastering physics

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Using the masses of the neutral atoms in your calculation accounts for the energy released by the annihilation of the positrons with electrons, so you rdaioactive work this problem without reference to the positrons or their rest mass. Part A Hafl is the total energy released in a single fusion reaction event for the equation given in the problem introduction? Express your answer in joules to two significant figures. How to approach the question Find the mass defect of the reaction ; then use. Using this number, find the number of proton-proton chain fusion reactions that must go on inside the sun in one second to release enough energy to balance the energy radiated away.

If this condition isn't met, the sun would cool off rapidly. Express your answer to two significant figures. Part C What mass of hydrogen is converted into helium by the fusion reactions in one second? Use for the mass of one hydrogen nucleus.

It had been social by Si Dirac inthough the glad of the glad was not too understood until the file discovery. Anon D Gusto the angular xi of the elements.

Express your answer in kilograms to two significant figures. What mass of hydrogen would have to be burned in the sun in one second to release the same amount of energy i. Relating mass of burned hydrogen and power Recall that one watt is equal to one joule per second. You are asked for the mass that must be burned in one second to generate the same energy as the sun generates in one second. Thus, the question is really asking what mass of hydrogen must be burned to generate. The heat of combustion gives the number of joules generated by burning one kilogram of hydrogen. Use this to find the number of kilograms of hydrogen that must be burned to generate.

Print View with Answers 5 of 20 https: At this rate, the sun would use up all of its hydrogen in only 17, years, instead of the roughly 5 billion years that solar physicists estimate for the sun's current fuel supply. Of course, this is just an abstraction since there is no supply of oxygen available for such "burning" to take place. Nineteenth-century physicists trying to determine the age of the sun based their calculations on how much energy the sun radiated. They immediately realized that chemical reactions could not produce nearly enough energy to account for the sun being more than a few thousand years old, an age directly contradicted by historical records.

The largest energy source that they could imagine was the gravitational energy of all the matter that formed the sun. Even this source was far too weak: Calculations based on gravitational energy only allowed the sun to be around 30 million years old, though it is, in fact, over 4. No nineteenthcentury physicist could have envisioned the incredible amounts of energy released by nuclear reactions. The first antiparticle, the positron or antielectron, was discovered in It had been predicted by Paul Dirac inthough the nature of the prediction was not fully understood until the experimental discovery.

Today, it is well accepted that all fundamental particles have antiparticles. Part A Which of the following are different for a particle and its antiparticle? Both have kinetic energy of 4. They produce two photons, which by conservation of momentum must have equal energy and move in opposite directions. What is the energy of one of these photons? Express your answer in to three significant figures. What is the minimum kinetic energy energy of a pion is. Express your answer in of one of these protons necessary to make a pion-antipion pair? The rest to three significant figures Hint 1.

Connecting kinetic energy to mass In a sufficiently violent particle collision, kinetic energy may be converted into the rest energy of new particles. All that is necessary is for the amount of kinetic energy available to meet or exceed the rest energy of the pair that you wish to produce. Available kinetic energy Because the two protons collide head-on with equal kinetic energy, the net momentum before the collision is zero. Print View with Answers 6 of 20 https: Several qualitative and quantitative questions: Focuses on classical model but last follow-up statement makes reference to relativistic model. To learn the basic physics and applications of cyclotrons. Particle accelerators are used to create well-controlled beams of high-energy particles.

Such beams have many uses, both in research and industry. One common type of accelerator is the cyclotron, as shown in the figure. In a cyclotron, a magnetic field confines charged particles to circular paths while an oscillating electric field accelerates them. It is useful to understand the details of this process. Consider a cyclotron in which a beam of particles of positive charge restricted by the magnetic field and mass is moving along a circular path which is perpendicular to the velocity of the particles. Part A Before entering the cyclotron, the particles are accelerated by a potential difference Express your answer in terms of.

Find the speed with which the particles enter the cyclotron. The magnitude of the magnetic field is Express your answer in terms of. Find the force Find the magnitude of the force acting on the particles. Express your answer in terms of,and. You may or may not use all these variables. Find the acceleration Find the magnitude of the acceleration Express your answer in terms of of the particles. Print View with Answers 7 of 20 https: Use Newton's second law to construct an equation to be solved for. Express your answer in terms of Hint 1. Relationship between, and. Since the speed of the particle is constant, the period will be equal to the distance the particle travels in one orbit divided by the particle's speed: Part D Find the angular frequency of the particles.

Express your answer in terms ofHint 1. Relationship betweenand. The angular frequency ; it is the number of radians the particle traverses per second. Find,and. What minimum radius of the cyclotron is required? Print View with Answers 8 of 20 https: If you can build a cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? Assume that the magnetic field remains the same. Find in terms of Using your result from Part E, solve for Express your answer in terms ofin terms of, and. Find in terms of and Using your result from Part E, solve for Express your answer in terms ofin terms of, and and.

When their speeds become comparable to the speed of lightthe angular frequency is no longer what you determined in Part D.

Using special relativity, one can show that the xating frequency datin actually given by masterkng formula. As you can see, the frequency drops as the energy and speed increases; the particles' motion falls Halr 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. A new particle accelerator facility is being built. The designers are considering two designs, one using msstering targets and the other using collisions of beams radioactivs 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 fating volts to three significant lfie. Print View with Answers 9 of 20 https: Formula for available energy Recall that the formula physicss available energy target particle, and iswhere 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. 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 datng track the number of strange particles in a hadron both mesons and baryons. If a particle has a strange quarkthen physkcs has strangeness. If the particle has an masterinng quarkthen it has strangeness. These numbers are additive; two strange quarks in combination means a strangeness rarioactive. Print View with Answers 11 of 20 https: The United States uses 1. Assume that all fission energy is converted into electrical energy. 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 Hal, energy released by, and number of beta and alpha decays involved in the Th decay chain. 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 bya 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? Women appearance and threats of sexual violence directed at her on mastering and twitter.

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