Assignment Key: Particle Radiation

Because there is a wide range of particle masses, charges and impact velocities, it is more difficult to compare the effect of various forms of particle radiation.

One useful method is to compare the amount of energy a particle yields when it collides with absorbing matter. Some particles yield most of their kinetic energy over short distances, others deplete their energy gradually over longer distances.

For each type of particle one can calculate a quantity called linear energy transfer or LET which defined as the total energy dissipated divided by the path length required for the particle to come to rest.

LET = E/l (J/m or keV/m)
where E is the kinetic energy of the incident particle and l is its stopping distance.

  1. Using the table Data Sheet of Particle Radiation, calculate the LET for a typical radioactive alpha particle in air.
    1.00x107keV/m

  2. Calculate the LET for a typical radioactive decay electron (beta particle) in air.
    1.00x105keV/m

  3. A primary solar cosmic ray proton travels 1km in the atmosphere. If its kinetic energy is 2GeV, what is its LET value in air?
    2.00x103keV/m

    Of course the linear energy transfer depends upon the chemical composition of the absorbing material and the density of the material. In the examples above, the density of air at sea level differs significantly from its density at high altitudes.

    For comparative purposes water is often chosen as the absorbing medium by which the LET of various types or radiation can be compared.

  4. A 600eV electron gives up its energy in water within a distance of 1.09x10-7m. Calculate its LET rate.
    5.5x106keV/m
  5. A 800keV proton gives up its energy in water within a distance of 1.77x10-5m. Calculate its LET rate.
    4.5x107keV/m
  6. A 5.3MeV alpha particle gives up its energy in water within a distance of 4.82x10-4m. Calculate its LET rate.
    1.19x108keV/m
  7. A 100 MeV fission fragment gives up its energy in water within a distance of 1.11x10-5m. Calculate its LET rate.
    9.00x109keV/m
    The nature of the radiation makes a considerable difference in the biological effects it creates even when the same amount of energy is absorbed. In general, the larger the value of the LET, the more biologically reactive the radiation.

    Of course the LET is only the average kinetic energy given up to the absorbing material over the particle's path and it tells little about the effects the added energy has on the absorbing material.

    The absorbed energy will usually cause ionizations to occur through particle-particle collisions when the energy of the incident particle exceeds the ionizing potential of the atoms it encounters.

  8. If the ionizing potential of a hydrogen atom is 10.6eV, how may ionizations will be created by an absorbed alpha particle if its incident kinetic energy of 100MeV is totally absorbed?
    9.4x104

  9. A general rule of thumb used by physicists is that about 30eV is needed for each ionization in liquid water whereby H2O is broken into H+ and OH-. How many ionizations are created in water by a single 800keV proton?
    2.67x105

  10. How many ionizations are created in water by a single 2GeV proton?
    6.67x109

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 how particle radiation interacts with matter by solving assignment problems with limited accuracy demonstrates some understanding of how particle radiation interacts with matter by solving assignment problems some accuracy demonstrates considerable understanding of how particle radiation interacts with matter by solving assignment problems with general accuracy demonstrates thorough understanding of how particle radiation interacts with matter by solving assignment problems with a high degree of accuracy
Inquiry

The student:
Level 1
Level 2
Level 3
Level 4
interprets and uses data relating to particle radiation with limited competence making major errors/omissions interprets and uses data relating to particle radiation with moderate competence making several minor errors/omissions interprets and uses data relating to particle radiation with considerable competence making few minor errors/omissions interprets and uses data relating to particle radiation 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,