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The sievert

Radiation and the atom · level 6, lesson 2 of 6

A question to start

One milligray of alpha radiation and one milligray of gamma rays put the same energy into the body. Do they do the same harm?

The idea

No. Alpha particles pack their energy into a short, dense track and damage cells far more. So the absorbed dose is multiplied by a radiation weighting factor for each kind of radiation. The result is the equivalent dose, in sieverts (Sv):

\[\text{equivalent dose (Sv)} = \text{absorbed dose (Gy)} \times \text{weighting factor}.\]

Canada's radiation rules use these factors:

Radiation Weighting factor
Gamma rays and X-rays 1
Electrons (beta) 1
Protons 2
Alpha particles and heavy nuclei 20
Neutrons depends on their energy

A second step weights each organ by how sensitive it is, giving the effective dose, also in sieverts. That is the number usually quoted. Everyday doses are given in millisieverts (mSv).

gammaprotonsalpha1 mSv2 mSv20 mSv

Each bar is the dose from 1 mGy of that radiation.

Worked examples

1. Gamma. 3 mGy of gamma rays: \(3 \times 1 = 3\) mSv.

2. Alpha. 3 mGy of alpha: \(3 \times 20 = 60\) mSv, twenty times the harm.

3. A mix in space. Suppose a crew member absorbs 0.4 mGy a day from protons and 0.05 mGy a day from heavy nuclei. \(0.4 \times 2 + 0.05 \times 20 = 0.8 + 1.0 = 1.8\) mSv a day. The heavy nuclei give only a small share of the energy but more than half of the harm.

Try it

  1. What is the unit of equivalent dose?
  2. Find the equivalent dose from 5 mGy of beta.
  3. Find the equivalent dose from 0.2 mGy of alpha.
  4. Why does alpha have a weighting factor of 20?
Answers
  1. The sievert, Sv.
  2. \(5 \times 1 = 5\) mSv.
  3. \(0.2 \times 20 = 4\) mSv.
  4. It puts its energy into a short, dense track, so it damages cells far more than the same energy of gamma rays.

Common mistake

Mixing up gray and sievert. The gray measures energy per kilogram. The sievert measures the harm that energy is likely to do. For gamma rays they come out the same number; for alpha, not at all.

Where it leads