National 5PhysicsSQARevision NotesRadiationNuclear RadiationEquivalent Dose

Equivalent Dose (SQA National 5 Physics): Revision Note

Exam code: X857 75

Leander Oates

Written by: Leander Oates

Reviewed by: Katie M

Updated on

Equivalent dose

  • Equivalent dose is a measure of how harmful a dose of radiation is

  • Equivalent dose can be calculated from the absorbed dose using the following relationship:

H space equals space D space cross times space w subscript R

  • Where:

    • H = equivalent dose, measured in sieverts (Sv)

      • 1 space Sv space equals space 1 space straight J space kg to the power of negative 1 end exponent

      • 1 space Sv is a large amount of energy, so doses tend to be given in millisieverts (mSv)

      • 1 space Sv space equals space 1000 space mSv

    • D = absorbed dose, measured in grays (Gy)

      • 1 space Gy space equals space 1 space straight J space kg to the power of negative 1 end exponent

    • w subscript R = radiation weighting factor

  • The radiation weighting factor accounts for the different types of radiation causing different degrees of biological harm

  • The amount of harm each type of radiation causes is linked to its relative ionising effect

  • The radiation weighting factors for different types of radiation are shown in the table

Radiation weighting factors

Type of radiation

Radiation weighting factor

alpha

20

beta

1

gamma

1

fast neutrons

10

slow neutrons

3

  • Radioactive sources frequently produce more than one type of radiation

  • In these instances, the radiation weighting factors of each type are added together

  • The key benefit to equivalent dose, is that 1 Sv of any type of radiation causes the same amount of damage

    • 1 mSv of alpha radiation is equal in damage to 1 mSv of gamma radiation

  • Equivalent dose is commonly used in medicine and nuclear safety to quantify exposure to radiation

Doctor in scrubs and lab coat standing behind a wheeled radiation shield with a warning symbol, holding a clipboard, indicating a medical setting.
Workers who are exposed to radiation use equivalent dose to monitor their exposure

Examiner Tips and Tricks

The radiation weighting factors are provided to you in the exam in the data sheet. You do not need to remember any values.

Equivalent dose rate

  • Equivalent dose rate is defined as:

The equivalent dose received per unit time of exposure to radiation

  • Equivalent dose rate can be calculated using the following relationship:

H with dot on top space equals space fraction numerator space H over denominator t end fraction

  • Where:

    • H with dot on top = equivalent dose rate, measured in sieverts per second (Sv s-1)

      • However, dose rates are often given in sieverts per hour (Sv hr-1)

    • H = equivalent dose, measured in sieverts (Sv)

    • t = time, measured in seconds (s)

      • However, seconds are usually not the most appropriate unit for measuring radiation doses, so hours, days, or even years are commonly used

  • Dose rates and exposure times often use larger units for time

    • For example:

      • Microsieverts per hour, μSv hr-1

      • Millisieverts per day, mSv day-1

      • Millisieverts per year, mSv yr-1

Worked Example

A radiation worker in a manufacturing facility is exposed to both gamma radiation and fast-moving neutrons over a period of 40.0 hours during one week.

The worker has a mass of 70.0 space kg.

They absorb 2.1 cross times 10 to the power of negative 4 end exponent space straight J of energy from gamma radiation.

They absorb 1.4 cross times 10 to the power of negative 5 end exponent space straight J of energy from fast moving neutrons.

(i) Determine the total equivalent dose received by the worker during this 40-hour period.

(ii) Calculate the equivalent dose rate received by the worker, in microsieverts per hour.

Answer:

List the known quantities:

  • Mass, m space equals space 70.0 space kg

  • Energy absorbed from gamma, E subscript gamma space equals space 2.1 cross times 10 to the power of negative 4 end exponent space straight J

  • Energy absorbed from fast-moving neutrons, E subscript f n end subscript space equals space 1.4 cross times 10 to the power of negative 5 end exponent space straight J

  • Radiation weighting factor for gamma, w subscript R space gamma end subscript space equals space 1

  • Radiation weighting factor for fast-moving neutrons, w subscript R space f n end subscript space equals space 10

(i) Determine the total equivalent dose received by the worker during this 40-hour period

Step 1: Calculate the absorbed dose from the gamma

  • Write out the appropriate relationship for absorbed dose

D subscript gamma space equals fraction numerator space E subscript gamma over denominator m end fraction

  • Substitute in the known values to calculate

D subscript gamma space equals space fraction numerator 2.1 cross times 10 to the power of negative 4 end exponent over denominator 70.0 end fraction

D subscript gamma space equals space 3.0 cross times 10 to the power of negative 6 end exponent space Gy

Step 2: Calculate the equivalent dose from gamma

  • Write out the appropriate relationship for equivalent dose

H subscript gamma space equals space D subscript gamma space cross times space w subscript R space gamma end subscript

  • Substitute in the known values to calculate

H subscript gamma space equals space open parentheses 3.0 cross times 10 to the power of negative 6 end exponent close parentheses space cross times space 1

H subscript gamma space equals space 3.0 cross times 10 to the power of negative 6 end exponent space Sv

Step 3: Calculate the absorbed dose from the fast-moving neutrons

  • Write out the appropriate relationship for absorbed dose

D subscript f n end subscript space equals space E subscript f n end subscript over m

  • Substitute in the known values to calculate

D subscript f n end subscript space equals space fraction numerator 1.4 cross times 10 to the power of negative 5 end exponent over denominator 70.0 end fraction

D subscript f n end subscript space equals space 2.0 cross times 10 to the power of negative 7 end exponent space Gy

Step 4: Calculate the equivalent dose from the fast-moving neutrons

  • Write out the appropriate relationship for equivalent dose

H subscript f n end subscript space equals space D subscript f n end subscript space cross times space w subscript R space f n end subscript

  • Substitute in the known values to calculate

H subscript f n end subscript space equals space open parentheses 2.0 cross times 10 to the power of negative 7 end exponent close parentheses space cross times space 10

H subscript f n end subscript space equals space 5.0 cross times 10 to the power of negative 6 end exponent space Sv

Step 5: Find the total equivalent doses

  • Add the equivalent doses of the gamma and fast-moving neutrons

H subscript t o t a l end subscript space equals space H subscript gamma space plus space H subscript f n end subscript

H subscript t o t a l end subscript space equals space open parentheses 3.0 cross times 10 to the power of negative 6 end exponent close parentheses space plus space space open parentheses 5.0 cross times 10 to the power of negative 6 end exponent close parentheses

H subscript t o t a l end subscript space equals space 5.0 cross times 10 to the power of negative 6 end exponent space Sv

(ii) Calculate the equivalent dose rate received by the worker, in microsieverts per hour

Step 1: Write out the appropriate relationship for equivalent dose rate

H with dot on top space equals fraction numerator space H subscript t o t a l end subscript over denominator t end fraction

Step 2: Convert the equivalent dose into microsieverts

  • micro = 10-6

  • μSv = 10-6 sV

5.0 cross times 10 to the power of negative 6 end exponent space Sv space cross times space fraction numerator 1 space straight mu Sv over denominator 1 cross times 10 to the power of negative 6 end exponent space Sv end fraction

H subscript t o t a l end subscript space equals space 5.0 space straight mu Sv

Step 3: Substitute in the known values to calculate

H with dot on top space equals space fraction numerator 5.0 space straight mu Sv over denominator 40.0 space straight h end fraction

H space equals space 0.125 space straight mu Sv space straight h to the power of negative 1 end exponent

Step 4: Round to an appropriate number of significant figures

  • The least precise input value is 2 s.f.

  • Therefore, the final answer can only be given to the same precision

H space equals space 0.13 space straight mu Sv space straight h to the power of negative 1 end exponent space open parentheses 2 space straight s. straight f. close parentheses

Examiner Tips and Tricks

You may not have to convert units of time into seconds unless the question asks you to do so. Check the units given in the question and the units required for the answer to determine if a conversion is required.

You can learn more about prefixes in the Revision Note SI Units & Prefixes

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    Author
    Reviewer
    Leander Oates

    Author: Leander Oates

    Expertise: Physics Content Creator

    Leander graduated with First-class honours in Science and Education from Sheffield Hallam University. She won the prestigious Lord Robert Winston Solomon Lipson Prize in recognition of her dedication to science and teaching excellence. After teaching and tutoring both science and maths students, Leander now brings this passion for helping young people reach their potential to her work at SME.

    Katie M

    Reviewer: Katie M

    Expertise: Physics Content Creator

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.