Answer to Question #6847 Submitted to "Ask the Experts"

Radium-beryllium (Ra-Be) sources were fabricated as neutron-emitting sources of the (α,n) type. They have the advantage that the decay of the ^₂₂₆Ra leads quickly to the alpha-emitting progeny ²²²Rn, ²¹⁸Po, and ²¹⁴Po that reach secular equilibrium with the alpha-emitting radium. These added alpha emitters extend in energy to 7.7 MeV, and the increased number of alpha particles per decay of ²²⁶Ra, along with the high energies, produce neutron yields per unit activity of the parent radionuclide that are considerably greater than what are observed for many other common (α,n) sources such as ²³⁹Pu-Be and ²⁴¹Am. Thus, the neutron yield from a ²²⁶Ra source may be approximately 4.6 x 10^-4 n s^-1 Bq^-1 of ²²⁶Ra (adapted from Herman Cember, Introduction to Health Physics, Pergamon Press, Table 5.5, 2^nd ed.; 1983) compared to a value about 10 times less for ²³⁹Pu-Be.

Unfortunately, the decay of ²²⁶Ra and its progeny is accompanied by significant gamma radiation emission that makes handling of ²²⁶Ra-Be sources more difficult and subject to more protection requirements than may be the case for other (α,n) sources. The gamma radiation air kerma rate constant at one meter for a lightly filtered ²²⁶Ra point isotropic source is about 5.38 x 10^-11 μGy m² s^-1 Bq^-1 (National Council on Radiation Protection and Measurements [NCRP] Report No. 112, Table 4.3; 1991). Using the neutron emission and gamma constant given here we can estimate the dose rate from your source; we shall assume it may be treated as a point isotropic source (p.i.s.) with respect to both neutron and gamma emission and shall not attempt to account for possible added attenuation or scatter from the source encapsulation. The assumption of a point source is reasonable as long as the distance from the source is several times the maximum source dimension.

To estimate the neutron dose equivalent rate we should recognize that practically all of the neutrons produced by the (µ,n) reactions on beryllium are relatively energetic neutrons. For the ²²⁶Ra-Be source the average neutron will expectedly be higher than that for a Pu-Be or Am-Be source, likely close to 5 MeV. Current U.S. Nuclear Regulatory Commission regulations use fluence-to-dose equivalent conversion factors (DCF) that are based on NCRP Report No. 38 (Protection Against Neutron Radiation, National Council on Radiation Protection and Measurements; 1991), and the DCF at 5 MeV is 2.3 x 10⁶ n cm^-2 mSv^-1. The neutron dose equivalent rate, H_n, is then given by the product of this DCF and the fluence rate, and the fluence rate at distance r from a p.i.s. emitting S n s^-1 is given by S/4πr². For the 781 mCi source we calculate

S = (781 mCi)(3.7 x 10⁷ Bq mCi^-1)(4.6 x 10^-4 n s^-1 Bq^-1) = 1.33 x 10⁷ n s^-1.

H_n = ((1.33 x 10⁷ n s^-1)/ 4π(100²))(1 mSv/2.3 x 10⁶ n-cm^-2)(3,600 s h^-1) = 1.7 x 10^-1 mSv h^-1 (17 mrem h^-1).

K_γ = (5.38 x 10^-11 μGy s^-1 m²/Bq)(781 mCi)(3.7 x 10⁷ Bq mCi^-1)(3,600 s h^-1)/(1 m)² = 5.6 x 10³ μGy h^-1.

If we assume a condition of secondary charged particle equilibrium, this kerma rate in air may be converted to dose equivalent rate in soft tissue by multiplying by the ratio of the mass energy absorption coefficient for tissue compared to air (for ²²⁶Ra gamma rays this ratio is about 1.11) and by the quality factor of 1.0 for gamma radiation.

Hγ = (5.6 x 10³ μGy h^-1)(1.11)(1 μSv/μGy) = 6.2 x 10³ μSv h^-1 = 6.2 mSv h^-1 (620 mrem h^-1).

H_total = H_n + H_γ = 1.7 x 10^-1 mSv h^-1 + 6.2 mSv h^-1 = 6.4 mSv h^-1 (640 mrem h^-1).