The Strontium 90 case. Official internal dose factors are like SS which name shower a chamber gas.

Strontium 90 (Strontian, Scotland); Sr; at.mass 89,907738; n° at. 38; m.p. 777°C; b.p. 1382°C; sp. gr. 2,54; half-life 28,78 years; 1,381E2 Ci/gr; β-; 0,546 MeV; range β- in tissues ~1645 μ.

 

The strontium 90 have a physical half-life of 28,78 years, a biological half-life of 34 years, an a effective half-life of 15,6 years.

(λ physic 7,637E-10, λ biologic 6,465E-10, λ effective 1,410E-9. The IRCP inhalation dose factor is 1,5E-7 Sv/Bq.)

Assessing the rationality of official internal dose factor or what body mass is necessary to explain the IRCP dose factor for this element ?

An absorbed dose is calculate taking account all the disintegrations that occurs in 50 years produce by the incorporation of a mass of matter which initially emitted 1 Bq. Then the incorporation of 1 Bq of strontium 90 conduce after 50 years to suffer (1 Bq/1,410E-9 λe) * 1-(EXP(50*31536000*-1,410E-9)) = 6,324E8 disintegrations β- and conduce to absorb 6,32E8 disintegrations * 0,546 MeV * 1,602E-13 Joule per MeV = 5,532E-5 Joule and 553,20804 Erg which dissipate, for IRCP, in a body mass of 368,81 kg... ((6,32E8 Emissions * 0,5460 MeV * 1,602E-6 Erg par MeV * 1 EBR)/(1,500E-7 Sv/Bq * 1 Bq * 100 Erg/gr * 100 Rad/Sv) = 368,81 kg) with a radius of (368805,3576 cm3/(4/3*3,14159))^(1/3) = 44,4873 cm.  The particle β- which penetrate no more than 1645 μ in tissues travel in rational calculation 270,4 times far away it can physically go... (444873,16 μ/1645 μ = 270,4.) In other words the real absorbed dose is reduce 19,78 millions times. (270,44^3 = 1,98E7 or 3,69E5 gr/1,86E-2 gr = 1,98E7.)

Calculating the dose produce by one β- particle with 0,546 MeV energy and 1645 μ penetration capacity in tissues:

(1 Bq * 0,5460 MeV * 1,602E-6 Erg per MeV * 1 EBR)/((4/3 * 3,14159 * (1645 * 0,0001^3)) gr * 100 Erg/gr * 100 Rad/Sv) = 4,69E-9 Sv/Bq or 4,69 nanoSievert per Becquerel. The committed dose for 1 Bq in 50 years is then (1 Bq/1,41E-9 λ effective s-1 * (1-Exp(50*365*24*60*60 * -1,41E-9 λ effective))) * 4,69E-9 Sv/Bq) = 2,9669 Sv/Bq or 2,97 Sievert per Becquerel.

Official internal dose factors are like SS which name shower a chamber gas.