The Physics
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Opus in profectus

# Mass-Energy

## Problems

### practice

1. Write something.
2. Write something.
3. Write something.
4. Write something completely different.

### numerical

1. The luminosity of the sun is 3.828 × 1026 W.
1. Determine the mass of the sun converted to energy in one second.
2. How many elephants is this?
2. Fermi National Accelerator Laboratory (a.k.a. Fermilab) in Batavia, Illinois is a US Department of Energy National Laboratory and home of the world's most powerful particle accelerator, the Tevatron, which accelerates beams of protons and antiprotons to ultra-high energy and brings them into head-on collision. Protons in the Tevatron's accelerator ring acquire energies on the order of 1012 elevtronvolts — a teraelectronvolt (TeV).
1. From the Tevatron's energy…
1. determine the speed of a proton in the accelerator
2. and then verify (or contradict) the laboratory's claim that protons "circle the four-mile [6.4 km] ring 57,000 times each second."
2. Determine the mass-energy of a proton-antiproton collision in the Tevatron in…
1. atomic mass units and
2. multiples of the proton's rest mass
3. ﻿Read the following excerpts about the the world's largest and most powerful particle accelerator, the Large Hadron Collider (LHC) at the European Organization for Nuclear Research (still called by its old acronym CERN) in Geneva, Switzerland.

LHC stands for Large Hadron Collider. Large due to its size (approximately 27 km in circumference), Hadron because it accelerates protons or ions, which are hadrons, and Collider because these particles form two beams travelling in opposite directions, which collide at four points where the two rings of the machine intersect.

The accelerator complex at CERN is a succession of machines with increasingly higher energies. Each machine injects the beam into the next one, which takes over to bring the beam to an even higher energy, and so on. In the LHC — the last element of this chain — each particle beam is accelerated up to the record energy of 7 TeV. In addition, most of the other accelerators in the chain have their own experimental halls, where the beams are used for experiments at lower energies.

No particle can move with speeds faster than the speed of light in a vacuum; however, there is no limit to the energy a particle can attain. In high-energy accelerators, particles normally travel very close to the speed of light. In these conditions, as the energy increases, the increase in speed is minimal. As an example, particles in the LHC move at 0.999997828 times the speed of light at injection (energy = 450 GeV) and 0.999999991 times the speed of light at top energy (energy = 7000 GeV). Therefore, particle physicists do not generally think about speed, but rather about a particle's energy.

Important parameters for the LHC * energy per nucleon
quantity number
circumference 26,659 m
dipole operating temperature 1.9 K (−271.3 °C)
number of magnets 9,593
number of main dipoles 1,232
number of RF cavities 8 per beam
nominal energy, protons 7 TeV
nominal energy, ions 2.76 TeV/u*
peak magnetic dipole field 8.33 T
min. distance between bunches ~7 m
design luminosity 1,034 cm−2 s−1
no. of bunches per proton beam 2,808
no. of protons per bunch (at start) 1.1 × 1011
number of turns per second 11,245
number of collisions per second 600 million

The total energy in each beam at maximum energy is about 350 MJ, which is about as energetic as a 400 t train, like the French TGV, travelling at 150 km/h. This is enough energy to melt around 500 kg of copper. The total energy stored in the LHC magnets is some 30 times higher (11 GJ).

CERN, 2008

Verify the following claims made in this FAQ.

1. "…particles in the LHC move at… 0.999999991 times the speed of light at top energy…"
1. Do it once using the dimensions of the LHC (easy, but less precise).
2. Do it again using the top energy value (not so easy, but more precise).
2. "The total energy in each beam at maximum energy is about 350 MJ…"
3. "…which is about as energetic as a 400 t train, like the French TGV, travelling at 150 km/h…"
4. "This is enough energy to melt around 500 kg of copper."
4. A standard measure of explosive energy is the ton of TNT. By definition, one ton of TNT possesses 4.184 gigajoules of chemical energy.
1. The "Little Boy" uranium fission bomb dropped on Hiroshima, Japan on 6 August 1945 had an explosive yield of 12.5 kilotons of TNT. How much mass was transformed into energy by this weapon? About how big is this?
2. The nuclear weapon with the greatest yield was the 50 megaton, two-stage fusion "Tsar Bomba" (Цар Бомба) detonated over Novaya Zemlya, Russia on 30 October 1961. How much mass was transformed into energy by this weapon? About how big is this?
5. A photon has just enough energy to form an electron-positron pair.
1. Write this reaction out in symbolic form.
2. What is the energy of this photon?
3. What is its frequency?
4. What is its wavelength?
5. What type of electromagnetic radiation is this?
6. A proton and an antiproton with very little kinetic energy come in contact with one another, annihilate, and produce two photons.
1. Write this reaction out in symbolic form
2. What is the energy of each photon?
3. What is the frequency of each photon?
4. What is the wavelength of each photon?
5. What type of electromagnetic radiation are these photons?