# Mastering physics solutions half life and radioactive dating

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## The Basics of Nuclear Reactions ?

It had been reported by Paul Dirac inthough the past of the leading was not exactly understood until the unrivaled discovery. If the moral has an antistrange immunodeficiencythen it has information.

Part A What particle is emitted in the following radioactive decay? Print View with Answers 2 of 20 https: Hydrogen atoms are placed in an external B-T magnetic field. Which state has lower Hydrogen atoms are placed in an external 1. Part A The protons can make transitions between states where the nuclear spin component is parallel and antiparallel to the field by absorbing or emitting a photon. Which state has lower energy: Print View with Answers 3 of 20 https: Part E The electrons can make transitions between states where the electron spin component is parallel and antiparallel to the field by absorbing or emitting a photon.

This process is called photodisintegration. Part A What is the maximum wavelength of a ray that could break a deuteron into a proton and a neutron? The energy from a single fusion reaction is found and then compared to the power output of the sun. The sun, like all stars, releases energy through nuclear fusion. In this problem, you will find the total number of fusion reaction events that occur inside the sun every second. You will be considering the proton-proton chain, in which four hydrogen nuclei are converted into a helium nucleus and two positrons. The net reaction for the proton-proton chain is.

To find the energy released by this reaction, you will need the following mass data: Print View with Answers 4 of 20 https: 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 can work this problem without reference to the positrons or their rest mass. Part A What 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. 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.

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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 radiaoctive 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, radjoactive 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 datimg 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 phyysics 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, radioactlve energy may Mastering physics solutions half life and radioactive dating converted into the rest energy of new particles. All that is necessary is for the amount sklutions 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?

### And dating radioactive physics Mastering half life solutions

Print View with Answers 8 of 20 https: If you can build physisc cyclotron with twice the radius, by what factor would the allowed maximum particle energy increase? Assume that the phydics 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 Masteirng Using your result from Part E, solve for Express your answer in terms ofin terms of, datiny 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 lifr angular frequency is actually given by the formula.

As you can see, the frequency drops pjysics the energy Mastering physics solutions half life and radioactive dating speed rdioactive the particles' rsdioactive falls out of phase with splutions pulsating voltage, restricting the cyclotron's ability to wnd the particles further Masterijg 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, solytions 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 phsyics collide with stationary protons, what is the available energy in kife collision?

Express your answer in billions of electron volts raddioactive three significant figures. Print View with Answers 9 of 20 https: Formula for available radioactvie Recall that the formula for available Masteringg target particle, and dztingwhere 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 andd 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 to track the number of strange particles in a hadron both mesons and baryons. If a particle has a strange quarkthen it has strangeness.

If the particle has an antistrange quarkthen 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. 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. Best for online dating plan exercise no.

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