Physics

6.5 - Radiation Dose

4 min

note 1 of 6

Absorbed dose

When ionising radiation is absorbed by a material, it transfers energy to it.
Absorbed dose ( $D$ ) is the energy absorbed per unit mass of the absorbing material.

Formula for absorbed dose

$D = \frac{E}{m}$

Where:

$D$ = Absorbed dose, in grays (Gy)
$E$ = Energy absorbed, in joules (J)
$m$ = Mass of absorbing material, in kilograms (kg)

Absorbed dose is measured in grays (Gy), where 1 Gy is 1 joule per kilogram.

note 2 of 6

Worked example - Energy absorbed by tissue

A sample of tissue with a mass of 4.0 kg receives an absorbed dose of 0.03 Gy after being exposed to a radioactive source. Calculate the energy absorbed by the tissue.

Step 1 - Formula

$D = \frac{E}{m}$

Step 2 - Rearrange the formula

$E = D \times m$

Step 3 - Substitution and calculation

$E = 0.03 \times 4.0 = 0.12 J$

The energy absorbed by the tissue is 0.12 J.

note 3 of 6

Equivalent dose and radiation weighting factor

The biological harm caused by radiation depends on the absorbed dose and the type of radiation.
Equivalent dose ( $H$ ) measures the biological effect of radiation on living tissue.

Radiation weighting factor

Each type of radiation has a radiation weighting factor ( $w_{r}$ ) that reflects how damaging it is:

Alpha - 20
Beta and gamma - 1

Formula for equivalent dose

$H = D w_{r}$

Where:

$H$ = Equivalent dose, in sieverts (Sv)
$D$ = Absorbed dose, in grays (Gy)
$w_{r}$ = Radiation weighting factor (no units)

Equivalent dose is measured in sieverts (Sv).

note 4 of 6

Worked example - Total equivalent dose

A sample of tissue receives an absorbed dose of 0.03 Gy of alpha radiation and 0.15 Gy of beta radiation. Calculate the total equivalent dose.

Step 1 - Formula

$H = D w_{r}$

Step 2 - Calculate the alpha equivalent dose

Alpha weighting factor = 20:

$H = 0.03 \times 20 = 0.6 Sv$

Step 3 - Calculate the beta equivalent dose

Beta weighting factor = 1:

$H = 0.15 \times 1 = 0.15 Sv$

Step 4 - Add the two equivalent doses

$Total H = 0.6 + 0.15 = 0.75 Sv$

The total equivalent dose is 0.75 Sv.

note 5 of 6

Formula for equivalent dose rate

$\dot{H} = \frac{H}{t}$

Where:

$\dot{H}$ = Equivalent dose rate, in sieverts per unit time (for example Sv/h)
$H$ = Equivalent dose, in sieverts (Sv)
$t$ = Time, in any unit of time (for example hours)

The equivalent dose rate ( $\dot{H}$ ) is the equivalent dose received per unit time.

note 6 of 6

Worked example - Equivalent dose rate

A person receives an equivalent dose of 90 μSv over a period of 3.0 hours. Calculate the equivalent dose rate in microsieverts per hour.

Step 1 - Identify the values

$H$ = 90 μSv
$t$ = 3.0 hours

Step 2 - Formula

$\dot{H} = \frac{H}{t}$

Step 3 - Substitution and calculation

$\dot{H} = \frac{90}{3.0} = 30 μSv/hour$

The equivalent dose rate is 30 microsieverts per hour.

key terms

TermDefinition

Absorbed doseThe energy absorbed from ionising radiation per unit mass of a material.

Equivalent doseA measure of the biological effect of radiation on living tissue, taking into account the type of radiation.

Radiation weighting factorA number that reflects how biologically damaging a specific type of radiation is.

Equivalent dose rateThe equivalent dose received by a material per unit of time.

end of notes

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6.6 - Comparing Radiation DoseNext up

Physics

6.5 - Radiation Dose

4 min

note 1 of 6

Absorbed dose

When ionising radiation is absorbed by a material, it transfers energy to it.
Absorbed dose ( $D$ ) is the energy absorbed per unit mass of the absorbing material.

Formula for absorbed dose

$D = \frac{E}{m}$

Where:

$D$ = Absorbed dose, in grays (Gy)
$E$ = Energy absorbed, in joules (J)
$m$ = Mass of absorbing material, in kilograms (kg)

Absorbed dose is measured in grays (Gy), where 1 Gy is 1 joule per kilogram.

note 2 of 6

Worked example - Energy absorbed by tissue

A sample of tissue with a mass of 4.0 kg receives an absorbed dose of 0.03 Gy after being exposed to a radioactive source. Calculate the energy absorbed by the tissue.

Step 1 - Formula

$D = \frac{E}{m}$

Step 2 - Rearrange the formula

$E = D \times m$

Step 3 - Substitution and calculation

$E = 0.03 \times 4.0 = 0.12 J$

The energy absorbed by the tissue is 0.12 J.

note 3 of 6

Equivalent dose and radiation weighting factor

The biological harm caused by radiation depends on the absorbed dose and the type of radiation.
Equivalent dose ( $H$ ) measures the biological effect of radiation on living tissue.

Radiation weighting factor

Each type of radiation has a radiation weighting factor ( $w_{r}$ ) that reflects how damaging it is:

Alpha - 20
Beta and gamma - 1

Formula for equivalent dose

$H = D w_{r}$

Where:

$H$ = Equivalent dose, in sieverts (Sv)
$D$ = Absorbed dose, in grays (Gy)
$w_{r}$ = Radiation weighting factor (no units)

Equivalent dose is measured in sieverts (Sv).

note 4 of 6

Worked example - Total equivalent dose

A sample of tissue receives an absorbed dose of 0.03 Gy of alpha radiation and 0.15 Gy of beta radiation. Calculate the total equivalent dose.

Step 1 - Formula

$H = D w_{r}$

Step 2 - Calculate the alpha equivalent dose

Alpha weighting factor = 20:

$H = 0.03 \times 20 = 0.6 Sv$

Step 3 - Calculate the beta equivalent dose

Beta weighting factor = 1:

$H = 0.15 \times 1 = 0.15 Sv$

Step 4 - Add the two equivalent doses

$Total H = 0.6 + 0.15 = 0.75 Sv$

The total equivalent dose is 0.75 Sv.

note 5 of 6

Formula for equivalent dose rate

$\dot{H} = \frac{H}{t}$

Where:

$\dot{H}$ = Equivalent dose rate, in sieverts per unit time (for example Sv/h)
$H$ = Equivalent dose, in sieverts (Sv)
$t$ = Time, in any unit of time (for example hours)

The equivalent dose rate ( $\dot{H}$ ) is the equivalent dose received per unit time.

note 6 of 6

Worked example - Equivalent dose rate

A person receives an equivalent dose of 90 μSv over a period of 3.0 hours. Calculate the equivalent dose rate in microsieverts per hour.

Step 1 - Identify the values

$H$ = 90 μSv
$t$ = 3.0 hours

Step 2 - Formula

$\dot{H} = \frac{H}{t}$

Step 3 - Substitution and calculation

$\dot{H} = \frac{90}{3.0} = 30 μSv/hour$

The equivalent dose rate is 30 microsieverts per hour.

key terms

TermDefinition

Absorbed doseThe energy absorbed from ionising radiation per unit mass of a material.

Equivalent doseA measure of the biological effect of radiation on living tissue, taking into account the type of radiation.

Radiation weighting factorA number that reflects how biologically damaging a specific type of radiation is.

Equivalent dose rateThe equivalent dose received by a material per unit of time.

end of notes

Key points to remember

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6.6 - Comparing Radiation DoseNext up