About 18% of a human\'s body mass is composed of carbon; some of this is radioac

Question

About 18% of a human's body mass is composed of carbon; some of this is radioactive carbon-14, a beta-emitter. If a 90 kg adult absorbs 100% of the 49 keV energy of each carbon-14 decay, what dose equivalent in Sv will they receive each decade from the carbon-14 decay in their body? (The chemical atomic mass of carbon, or average mass of all carbon atoms in the universe, is 12.011 u. Only one out of every trillion carbon atoms is in the form of carbon-14. Remember that the abundance of carbon-14 in living things remains constant throughout their lifetime as they exchange carbon with their environment.)

Explanation / Answer

Hi,
18% of body mass is Carbon.
So 90kg person has : 18x 90 / 100 = 16.2 kg of carbon.
Total number of carbon atoms :
1 amu = 1.66 x 10^-27 kg

1 carbon weighs 12 amu.
12 amu = 19.92 x 10^-27 kg = 20 x 10^-27 kg
20 x 10^-27 kg = 1 carbon
16.2 kg = ?
= 0.81 x 10^27 carbons.
= 81 x 10^25 carbons

1 in 10^12 carbon is C 14. ( 1 in one trillion; 1 trillion = 10^12)
so in 10^25 , we have 10^13 C14 atoms. ( 10^25 / 10612)
each C14 releases 49Kev during its fission. In 1 second 2 atoms undergo fission (given the half lf of Carbon is 5700 years). so in 10 years we have 3.15 x 10^8 seconds. So in total 7 x 10^8 atoms undergo fission. So the person absorbs 49 x 7 x 10^8 = 343 x 10^8 Kev. =343 x 10^5 Mev.
6.24 x 10^5 Mev = 1 erg; so 343 x 10^5 Mev = 54.96 erg. = 55 erg
10^7 erg = 1 joule
So 55 erg = 55 x10^-7 joule
1 joule= 1 Sv
so 55 x 10^-7 joule = 55 x 10^-7 SV

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