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Absorbed dose

Radiation and the atom · level 6, lesson 1 of 6

A question to start

A dose of radiation that makes a person ill puts less energy into their body than a sip of hot tea. How can so little energy do so much harm?

The idea

The absorbed dose is the radiation energy absorbed by each kilogram of material:

\[\text{absorbed dose} = \frac{\text{energy absorbed (J)}}{\text{mass (kg)}}.\]

Its unit is the gray (Gy): 1 Gy is 1 joule absorbed by each kilogram. Everyday doses are tiny, so they are given in milligrays (mGy), thousandths of a gray.

A gray is very little energy as heat. The harm comes from how the energy arrives: in sharp, separate hits, each one enough to knock electrons out of atoms and break molecules like DNA.

1 joule of radiation1 kgdose: 1 Gy

Worked examples

1. A whole body. Suppose a person of 70 kg absorbs 1 Gy. The energy is \(1 \times 70 = 70\) J.

2. As heat. Water needs about 4,200 J to warm 1 kg by 1 °C. The body is mostly water, so 70 J warms 70 kg by about \(70 \div (70 \times 4{,}200) \approx 0.0002\) °C. Nobody could feel that.

3. A small dose. A hand of 0.5 kg absorbs 0.001 J. Dose \(= 0.001 \div 0.5 = 0.002\) Gy, which is 2 mGy.

Try it

  1. What does 1 gray mean?
  2. A 2 kg block absorbs 0.01 J. Find the dose in mGy.
  3. How much energy does a 60 kg person absorb from a dose of 3 mGy?
  4. Why can a dose with so little energy be harmful?
Answers
  1. 1 joule of radiation energy absorbed by each kilogram.
  2. \(0.01 \div 2 = 0.005\) Gy, which is 5 mGy.
  3. \(0.003 \times 60 = 0.18\) J.
  4. The energy comes in separate hits that each break molecules, such as DNA.

Common mistake

"Dose is the total energy." Dose is energy per kilogram. A small child and an adult in the same beam get the same dose, though the adult absorbs more energy in total.

Where it leads