Assignment Key: Particle Radiation

The energy transported by particle radiation depends in large measure upon their kinetic energy and hence the velocity of the particles.

Particles such as protons are a major constituent of cosmic radiation. Some of these protons arrive in the solar system from distant sources in the galaxy. The majority however are arriving at the earth from the solar wind.

The graphs below show the kinetic energy of protons as a function of their velocity.


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1. Using the graph to the left determine the kinetic energy of a proton moving at 20% the speed of light. Express your answer in MeV.
2x107 eV or 20MeV

2. Using the graph to the left determine the kinetic energy of a proton moving at 40% the speed of light. Express your answer in MeV.
8x107 eV or 80MeV. Point out to students that doubling the velocity (from question 1) gives four times the kinetic energy...consistent with classical physics Ek=1/2mv2.

3. A proton is brought to rest by colliding it with atoms inside a very sensitive calorimeter. The proton releases 25MeV of energy. What was its initial impact velocity?
About 0.22c-0.23c

4. A substance absorbs a beam of 1011 protons. If the beam is monochromatic1 (i.e. all protons have exactly the same energy) and the velocity of the protons is 35% the speed of light (0.35c), how much energy is absorbed in MeV?
1011 x 6.5x107 = 6.5x1018eV = 6.5x1012MeV

1The term monochromatic, when used in particle physics, refers to the energy of an ensemble of particles, meaning they all have exactly the same energy. The term has been "borrowed" from optical physics.

5. Calculate the rate of energy transfer (power in watts) of the beam in question (4) if the protons are all absorbed within 10-5 seconds. (Recall 1eV=1.60x10-19J and 1W=1J/s)
6.5x1022MeV = 1.04x104J
1.04x104J in 10-5s = 1.04x109W or 1.04GW


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6. Using the graph to the left determine the kinetic energy of a proton moving at 60% the speed of light. Express your answer in MeV.
2.5x108eV = 2.5x102MeV

7. Using the graph to the left determine the kinetic energy of a proton moving at 98% the speed of light. Express your answer in MeV.
About 2x1011eV = 2x105MeV. Point out to students that at this velocity classical physics begins to break down, and the relativistic mass of the proton becomes important.

8. A proton is brought to rest by colliding it with atoms inside a very sensitive calorimeter. The proton releases 6GeV of energy. What was its initial impact velocity? About 0.95c

9. What factors, other than impact velocity, do you think determine the total amount of energy deposited by particle radiation when it irradiates a substance?
The mass of the particle, its charge (if any), its physical size, as well as the physical and chemical properties of the irradiated material.

10. Astronauts in space are subject to particle radiation from various celestial sources including the sun which ejects a high velocity stream of protons into space. The solar proton flux is highly variable and has the potential to deliver lethal doses of radiation to both humans and electronic equipment aboard various spacecraft.

Suggest several ways by which one might protect oneself and sensitive electric equipment from dangerous solar radiation.
Various techniques have been tried, these include:

  1. moving the spacecraft to a lower orbit, which provides both (limited) atmospheric shielding and magnetospheric shielding;
  2. surrounding the spacecraft or critical parts with thick radiation absorbing materials;
  3. and where possible, avoiding space missions when the sun is predicted to be dangerously active.


ASSESSMENT

The chart that follows identifies four levels of achievement for assessing students' communication of information and ideas. Levels 1 and 2 describe performance that is approaching the standard for the grade; level 3 describes the standard for the grade; and level 4 describes performance that is above the standard. In numerical terms, all four levels are at passing level for the grade. Level 1 corresponds to a mark of 50%-59%; level 2, 60%-69%; level 3, 70%-79%; and level 4, 80%-100% . Student performance that is not approaching or is significantly below the standard would receive a failing grade.

Understanding of Basic Concepts

The student:

Level 1
Level 2
Level 3
Level 4
demonstrates limited understanding of energy transported by particle radiation by solving problems related to the kinetic energy of protons with limited accuracy demonstrates some understanding of energy transported by particle radiation by solving problems related to the kinetic energy of protons with some accuracy demonstrates considerable understanding of energy transported by particle radiation by solving problems related to the kinetic energy of protons with general accuracy demonstrates thorough understanding of energy transported by particle radiation by solving problems related to the kinetic energy of protons with a high degree of accuracy
Inquiry

The student:

Level 1
Level 2
Level 3
Level 4
interprets and uses graphs relating to kinetic energy of a proton with limited competence making major errors/omissions interprets and uses graphs relating to kinetic energy of a proton with moderate competence making several minor errors/omissions interprets and uses graphs relating to kinetic energy of a proton with considerable competence making few minor errors/omissions interprets and uses graphs relating to kinetic energy of a proton with a high degree of competence making practically no errors/omissions
Communication of Information and Ideas

The student:

Level 1
Level 2
Level 3
Level 4
uses scientific terminology, symbols, conventions, and SI units with limited accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with some accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with considerable accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with a high degree of accuracy and effectiveness


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Prepared by the YES I Can! Science Team,