Equivalent Dose (SQA National 5 Physics): Revision Note

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

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 $70.0\mathrm{kg}$.

They absorb $2.1\times {10}^{-4}\mathrm{J}$ of energy from gamma radiation.

They absorb $1.4\times {10}^{-5}\mathrm{J}$ 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, $m=70.0\mathrm{kg}$

• Energy absorbed from gamma, $E_{\gamma }=2.1\times {10}^{-4}\mathrm{J}$

• Energy absorbed from fast-moving neutrons, $E_{fn}=1.4\times {10}^{-5}\mathrm{J}$

• Radiation weighting factor for gamma, $w_{R\gamma }=1$

• Radiation weighting factor for fast-moving neutrons, $w_{Rfn}=10$

(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

$D_{\gamma }=\frac{E_{\gamma }}{m}$

• Substitute in the known values to calculate

$D_{\gamma }=\frac{2.1\times {10}^{-4}}{70.0}$

$D_{\gamma }=3.0\times {10}^{-6}\mathrm{Gy}$

Step 2: Calculate the equivalent dose from gamma

• Write out the appropriate relationship for equivalent dose

$H_{\gamma }=D_{\gamma }\times w_{R\gamma }$

• Substitute in the known values to calculate

$H_{\gamma }=\left(3.0\times {10}^{-6}\right)\times 1$

$H_{\gamma }=3.0\times {10}^{-6}\mathrm{Sv}$

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

• Write out the appropriate relationship for absorbed dose

$D_{fn}=\frac{E_{fn}}{m}$

• Substitute in the known values to calculate

$D_{fn}=\frac{1.4\times {10}^{-5}}{70.0}$

$D_{fn}=2.0\times {10}^{-7}\mathrm{Gy}$

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

• Write out the appropriate relationship for equivalent dose

$H_{fn}=D_{fn}\times w_{Rfn}$

• Substitute in the known values to calculate

$H_{fn}=\left(2.0\times {10}^{-7}\right)\times 10$

$H_{fn}=5.0\times {10}^{-6}\mathrm{Sv}$

Step 5: Find the total equivalent doses

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

$H_{total}=H_{\gamma }+H_{fn}$

$H_{total}=\left(3.0\times {10}^{-6}\right)+\left(5.0\times {10}^{-6}\right)$

$H_{total}=5.0\times {10}^{-6}\mathrm{Sv}$

(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

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

Step 2: Convert the equivalent dose into microsieverts

• micro = 10^-6

• μSv = 10^-6 sV

$5.0\times {10}^{-6}\mathrm{Sv}\times \frac{1\mathrm{\mu Sv}}{1\times {10}^{-6}\mathrm{Sv}}$

$H_{total}=5.0\mathrm{\mu Sv}$

Step 3: Substitute in the known values to calculate

$\dot{H}=\frac{5.0\mathrm{\mu Sv}}{40.0\mathrm{h}}$

$H=0.125\mathrm{\mu Sv}{\mathrm{h}}^{-1}$

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

$H=0.13\mathrm{\mu Sv}{\mathrm{h}}^{-1}\left(2\mathrm{s}.\mathrm{f}.\right)$

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