Uranium 238 (Uranus); U; at. mass 238,0289; at. n° 92; m.p. 1135°C; b.p. 4131°C; sp. gr. ~18,95; half-life 4,49 billions years; 3,35E-7 Ci/gr; 2,99 tons/Ci; α decay; 4,184 MeV; alpha 4,184 MeV particle range in tissues ~50 μ.
The uranium 238 have a physical half-life of 4,49 billions years, a biological half-life for insoluble form (industrial depleted uranium) of 5 years and a effective half-life of 5 years.
(λ physic 4,895E-18, λ biologic 4,396E-9, λ effective 4,396E-9.)
The IRCP inhalation dose factor for U238 is 7,3E-6 Sv/Bq or 7,3 μSv/Bq.
Assessing the irrationality of official internal dose factor.
I: An beta or alpha internal dose determination is some kind of "poison dilution" calculation in a tiny histological volume which radius is equal to particle trajectory in matter. A ionizing dose damage is then nothing else than a cinematic energy divide by the volume of matter that this cinematic energy can penetrate. Shorter is particle trajectory, minor is volume impacted and higher is dose intensity. In alpha case this "poison dilution" is confined in an histological volume of ~50 μ radius and for instance the ionization of this tiny volume is extremely high. (For a same poisoning energy bigger is the "absorbing" volume lower is the dose intensity absorb (10/10 = 1) and lower is the "absorbing" volume bigger is the dose intensity absorb (10/1 = 10). Choose the correct volume is for instance crucial and overestimate the volume is underestimated the ionizing impact.)
II: Contrary to external dose factor which quantify the damage of a single disintegration, internal committed Sv/Bq dose factor quantify the damage for all "effective" disintegrations that occurs in body in 50 years produce by 1 Bq of a specific radioelement mass.
III: For decompose a internal dose factor 3 steps are necessary.
First step. Calculate 50 years radioactive emissions inside body taking account the effective period (ie. the biological elimination in 50 years of 82,5% of incorporated U238 atoms before they disintegrate in body), convert this MeV energy in Erg and multiply by RBE (1 for γ and β, 10 for α).
Second step. Knowing the Erg energy liberate in 50 years by remaining U238 atoms divide by official Sv/Bq integrating in denominator the fact that 1 Rad = 100 Erg/gr and 1 Sv = 100 Rad (in short multiply the Sv/Bq denominator by 10000) for determinate the body mass (gr.) which correspond to official dose factor. (Energy/Mass = Dose then Energy/Dose = Mass. 10/2 = 5 --> 10/5 = 2. No more.)
Third step. Is the calculate "absorbing" mass physically compatible with 50 μ penetration capacity of an alpha particle ?
An absorbed internal dose factor 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 U238 conduce after 50 years to suffer (1 Bq/4,396E-9 λe) * 1-(Exp(50*365*24*60*60*-4,396E-9)) = 2,273E8 "effective" disintegrations α and then absorb 2,27E8 disintegrations * 4,184 MeV * 1,602E-13 Joule per MeV = 1,523E-3 Joule and 15234,53 Erg which dissipate, for IRCP, in a fat body human mass of 208,69 kg...
(2,27E8 Emissions * 4,184 MeV * 1,602E-6 Erg/MeV * 10 RBE)/(7,3E-6 Sv/Bq * 1 Bq * 100 Erg/gr * 100 Rad/Sv) = 208,69 kg).
This enormous mass have a radius of (208692,2037 cm3/4/3*3,14159)1/3 = 36,79 cm. The particle α which penetrate no more than 50 μ in tissues travel in "rational" calculation 7359,3 times far away it can physically go... (367964,46 μ/50 μ = 7359,3...)
In other words the real absorbed dose is artificially diluted 398,57 billions times ! (7359,33 = 3,98E11 or 2,08E5 gr/5,24E-7 gr = 3,98E11.)
NB. Alternative way.
I: Determinate IRCP Sv/Bq for 1 disintegration dividing committed Sv/Bq by "effective decays" in 50 years. 7,3E-6/2,274702693E8 = 3,21E-14 Sv per disintegration. ((7,3E-6 Sv/Bq/((1 Bq/4,396E-9 λe) * 1-Exp(50*365*24*60*60*-4,396E-9 λe)) = 3,21E-14 Sv per disintegration.)
II: Calculate body mass for explain this dose value for one alpha particle of 4,184 MeV. ((1 Emission * 4,184 MeV * 1,602E-6 Erg/MeV * 10 RBE)/(3,21E-14 Sv/Bq * 100 Erg/gr * 100 Rad/Sv) = 208,69 kg).
Calculating the real dose produce by one α particle with 4,184 MeV energy and 50 μ penetration capacity in tissues:
(1 Bq * 4,184 MeV * 1,602E-6 Erg/MeV * 10 EBR)/((4/3 * 3,14159 * (50 * 0,00013)) gr * 100 Erg/gr * 100 Rad/Sv) = 0,0128 Sv/Bq or 12,8 milliSievert per disintegration. The committed dose for 1 Bq in 50 years is then (1 Bq/4,396E-9 λe s-1 * (1-Exp(50*365*24*60*60*-4,396E-9 λe))) * 1,28E-2 Sv/Bq) = 2,91E6 Sv/Bq or 2,91 millions Sievert per Becquerel.
Internal dose factors are false and criminally underestimated. They are obtain by the denominator falsification of the Energy/Mass equation. But nobody know and nobody care because most don't know "how a dose factor is arithmetically made". In this fundamental aspect for life universities organize the ignorance and promote the collective internal suicide. Low dose is a scientific fake, slow mass killing by internal contamination a fact. This past 30 years during peacekeeping wars thousand and thousand and thousand tons of depleted uranium have been aerosolized in flying nanometer atomic particles disseminate in all the world atmosphere that enter in each lung they encounter (in fake scientists lungs too ! Smile !) Official dose factors are like SS which name shower a chamber gas.
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