Answer :
A 50-kg human would be exposed to around 2.16 * 10^(-11) J/kg or 2.16 * 10^(-11) rads per year from the 14C naturally found in their body.
To calculate the number of rads received by a 50-kg human from the 14C naturally present in her body, we need to consider the decay of 14C and the energy released per disintegration.
First, we calculate the number of disintegrations per second:
Number of disintegrations = (mass of 14C / molar mass of 14C) * Avogadro's number
= (10^(-8) g / 14 g/mol) * (6.022 * 10^23 disintegrations/mol)
≈ 4.30 * 10^12 disintegrations per second
Next, we calculate the energy released per second:
Energy released = (number of disintegrations per second) * (energy per disintegration)
= (4.30 * 10^12 disintegrations/s) * (0.156 MeV/disintegration) * (1.602 * 10^(-13) J/MeV)
≈ 1.08 * 10^(-9) J/s
Finally, we calculate the absorbed dose in rads:
Absorbed dose (in rads) = (energy released per second) / (mass of the human)
= (1.08 * 10^(-9) J/s) / (50 kg)
≈ 2.16 * 10^(-11) J/kg
Therefore, a 50-kg human would receive approximately 2.16 * 10^(-11) J/kg or 2.16 * 10^(-11) rads per year from the naturally present 14C in her body.
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