The Americium 241 case. Official internal dose factors are like SS which name shower a chamber gas.

The americium 241 (from Americas); Am; atomic mass 241,056822; atomic n° 95; melting point 1176°C; boiling point 2011°C; specific gr. 13,67 (20°C); period of 432 years; 3,435 Ci/gr; 0,29 gr/Ci; α; 5,476 MeV; range particle in tissues ~50 μ. 

NB. 0,693147*6,0221415E+23/(241*432*365,25*24*60*60) = 1,270E11 Bq/gr or 3,4338 Ci/gr and 0,2912 gr/Ci.

Or (0,693147/(432*365,25*24*60*60)) * (6,0221415E+23/241) = 5,084E-11 λ * 2,4988E21 = 1,2705E11 Bq/gr

Or more simply 0,693147*6,0221415E+23/(365,25*24*60*60) = 1,322734E16 --> 1,322734E16/(241 * 432) = 1,270E11 Bq/gr  (0,693147*6,0221415E+23/(365,25*24*60*60*37E9) = 357495,6203 --> 357495,6203/(241 * 432) = 3,434 Ci/gr)

Or (6,0221415E+23/241)*(1-(Exp(1*-Ln(2)/(432*365,25*24*60*60)))) = 1,270E11 Bq/gr 

The americium 241 have a physical half-life of 432 years, a biological half-life of 200 years, an effective half-life of 136,7 years.

(λ physic 5,086E-11, λ biologic 1,099E-10, λ effective 1,608E-10.)

Assessing the irrationality of official internal dose factor. Or what body mass is necessary to explain the IRCP dose factor for this element ? 

An internal dose factor (Sv/Bq) is calculate taking account all the “effectives” disintegrations that occurs in 50 years produce by the incorporation of a matter mass which initially emitted 1 Bq.

The incorporation of 1 Bq of americium 241 conduce after 50 years to suffer (1 Bq/1,608E-10 λe) * 1-(EXP(50*31536000*-1,608E-10)) = 1,393E9 disintegrations α and absorb 1,39E9 disintegrations * 5,476 MeV * 1,602E-13 Joule per MeV = 0,0122 Joule and 122200 Erg which dissipate, for IRCP, in a body mass of 313,33 kg... ((1,39E9 Emissions * 5,4760 MeV * 1,602E-6 Erg par MeV * 10 EBR)/(3,900E-5 Sv/Bq * 1 Bq * 100 Erg/gr * 100 Rad/Sv) = 313,33 kg) with a radius of (313333,3587 cm3/(4/3*3,14159))^(1/3) = 42,1347 cm.  The particle α which do not penetrate in tissues more than 50 μ travel in “rational” calculation 8426,9 times far away it can physically go... (421346,45 μ/50 μ = 8426,9.) In other words the real absorbed dose is reduce 598,42 billions times. (8426,93³ = 5,98E11 or 3,13E5 gr/5,24E-7 gr = 5,98E11.)

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Calculating the real dose produce by one α particle with 5,476 MeV energy and 50 μ penetration capacity in tissues: (1 Bq * 5,4760 MeV * 1,602E-6 Erg par MeV * 10 EBR)/((4/3 * 3,14159 * (50 * 0,0001³)) gr * 100 Erg/gr * 100 Rad/Sv) = 1,68E-2 Sv/Bq or 16,76 milliSievert per Becquerel. The committed dose for 1 Bq in 50 years is then (1 Bq/1,608E-10 λe s-1 * (1-Exp(50*365*24*60*60 * -1,608E-10 λe))) * 1,68E-2 Sv/Bq) = 2,33E7 Sv/Bq or 23,34 millions Sievert per Becquerel.  Have a nice smell.

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

Cesium case
Strontium case
Uranium Case
Plutonium case
Tritium case