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Mean energy imparted by ionizing radiation per unit mass; its unit is the gray.

The idealized external photon estimate is approximately $0.557 mSv h^{- 1}$ at one metre. First apply radioactive decay to the certified radioactive activity:

A = 2.4 \times 1 0^{9} 2^{- 3/5.27} = 1.61751 \times 1 0^{9} Bq .

Treat the source as isotropic and small compared with the observation distance. Neglect photon self-absorption, capsule attenuation and attenuation in air. The metal and capsule stop the primary beta particles, so the direct external contribution is taken to be the two gamma rays; secondary bremsstrahlung is neglected. Their total energy per transformation is

E_{γ} = (1.17 + 1.33) MeV = 4.00544 \times 1 0^{- 13} J .

r

is therefore

Ψ_{E} (r) = \frac{A E _{γ}}{4 π r ^{2}} .

Interpret the given

3 m^{- 1}

μ_{en}

, rather than a total photon-removal coefficient. For an absorbing medium of mass density

ρ

S d x

absorbs energy per time

Ψ_{E} S μ_{en} d x

and has mass

ρS d x

. Its absorbed dose rate is consequently

\dot{D} = Ψ_{E} \frac{μ _{en}}{ρ} .

For the estimate assume a water-like

ρ = 1 0^{3} kg m^{- 3}

and local deposition of the secondary charged-particle energy. At

r = 1 m

\dot{D} = \frac{( 1.61751 \times 1 0 ^{9} ) ( 4.00544 \times 1 0 ^{- 13} )}{4 π} \frac{3}{1000} = 1.54671 \times 1 0^{- 7} Gy s^{- 1} = 0.556815 mGy h^{- 1} .

For gamma rays, the radiation weighting factor is one, giving $\dot{H} = 0.556815 mSv h^{- 1}$ under these assumptions.^[ref]

The phrase “equivalent absorbed dose” mixes two quantity names: absorbed dose is measured in gray, while equivalent dose is measured in sievert. Their rates are numerically equal here because the weighting factor is one. The estimate is a physical energy-deposition calculation; the assumed mass density is essential, and the stated inverse-length coefficient must not be used as if it already had area-per-mass units.

Sievert 2026-10-20

The SI unit used for equivalent dose and effective dose. Sharing dimensions with the gray does not make the quantities interchangeable.^[ref]