33.3 Accelerators create matter from energy  (Page 4/10)

Which of the below was the first hint that conservation of mass and conservation of energy might need to be combined into one concept?

1. The Van de Graaff generator.
2. New particles showing up in accelerators.
3. Yukawa's theory.
4. They were always related.

How fast would two 7.0-kg bowling balls each have to be going in a collision to have enough spare energy to create a 0.10-kg tennis ball? (Ignore relativistic effects.) Can you explain why we don't see this in daily situations?

Use the information in [link] to answer the following questions.

Taking only energy and mass into consideration, what is the minimum amount of kinetic energy a K ^- must have when colliding with a stationary proton to produce an Ω?

1. 240.5 MeV
2. 120.0 MeV
3. 15.5 MeV
4. 57.6 GeV

Using only energy-mass considerations, how many K ⁰ could a Z boson decay into? How many electrons and positrons could be produced this way?

A π ⁺ and a π ^- are moving toward each other extremely slowly. When they collide, two π ⁰ are produced. How fast are they going? (Ignore relativistic effects.)

1. Barely moving
2. 1.0×10 ⁷ m/s
3. 2.0×10 ⁷ m/s
4. 7.8×10 ⁷ m/s

Assume that when a free neutron decays, it transforms into a proton and an electron. Calculate the kinetic energy of the electron.

The total energy in the beam of an accelerator is far greater than the energy of the individual beam particles. Why isn't this total energy available to create a single extremely massive particle?

Synchrotron radiation takes energy from an accelerator beam and is related to acceleration. Why would you expect the problem to be more severe for electron accelerators than proton accelerators?

What two major limitations prevent us from building high-energy accelerators that are physically small?

What are the advantages of colliding-beam accelerators? What are the disadvantages?

At full energy, protons in the 2.00-km-diameter Fermilab synchrotron travel at nearly the speed of light, since their energy is about 1000 times their rest mass energy.

(a) How long does it take for a proton to complete one trip around?

(b) How many times per second will it pass through the target area?

Suppose a $W^{-}$ created in a bubble chamber lives for $5\text{.}\text{00}\times {\text{10}}^{-\text{25}}\text{s}.$ What distance does it move in this time if it is traveling at 0.900 c ? Since this distance is too short to make a track, the presence of the $W^{-}$ must be inferred from its decay products. Note that the time is longer than the given $W^{-}$ lifetime, which can be due to the statistical nature of decay or time dilation.

What length track does a ${\pi }^{+}$ traveling at 0.100 c leave in a bubble chamber if it is created there and lives for $2\text{.}\text{60}\times {\text{10}}^{-8}\text{s}$ ? (Those moving faster or living longer may escape the detector before decaying.)

The 3.20-km-long SLAC produces a beam of 50.0-GeV electrons. If there are 15,000 accelerating tubes, what average voltage must be across the gaps between them to achieve this energy?

Because of energy loss due to synchrotron radiation in the LHC at CERN, only 5.00 MeV is added to the energy of each proton during each revolution around the main ring. How many revolutions are needed to produce 7.00-TeV (7000 GeV) protons, if they are injected with an initial energy of 8.00 GeV?

A proton and an antiproton collide head-on, with each having a kinetic energy of 7.00 TeV (such as in the LHC at CERN). How much collision energy is available, taking into account the annihilation of the two masses? (Note that this is not significantly greater than the extremely relativistic kinetic energy.)

When an electron and positron collide at the SLAC facility, they each have 50.0 GeV kinetic energies. What is the total collision energy available, taking into account the annihilation energy? Note that the annihilation energy is insignificant, because the electrons are highly relativistic.