Assume a liter of milk typically has an activity of 2000 pCi due to 4019K. If a

Question

Assume a liter of milk typically has an activity of 2000 pCi due to 4019K. If a person drinks two glasses (0.5 L) per day, estimate the total effective dose (in Sv and in rem) received in a year. As a crude model, assume the milk stays in the stomach 12 hr and is then released. Assume also that very roughly 10% of the 1.5 MeV released per decay is absorbed by the body.

1.) Estimate the total effective dose in Sv/year for a 90-kg adult. Estimate the total effective dose in rem/year for a 90-kg adult. Compare your result to the normal allowed dose of 100 mrem per year. Estimate the total effective dose in Sv/year for a 8-kg baby.Estimate the total effective dose in rem/year for a 8-kg baby.Compare your result to the normal allowed dose of 100 mrem per year.

Explanation / Answer

liter of milk typically has an activity,(A) of 2000 x 10-12 Ci due to 4019K. the rate at which energy emitted is given as:

P = (2000 x 10-12 Ci/L) (3.7 x 1010 decay/sec-Ci) (1.5 MeV/decay) (1.6 x 10-13 J/MeV)

P = 1.77 x 10-11 J/s-L

If 10% of the 1.5 MeV released per decay is absorbed by the body for (12 h/day), then the toatal absorbed energy rate is given as ::

R = (0.10) (1.77 x 10-11 J/s-L) (0.5 L)1/2 (3.16 x 107 Sv/year)

R = 1.4 x 10-5 J/year

(1) total effective dose in Sv/year for a 90-kg adult is given as ::

dose = (1.4 x 10-5 J/year) (1) / (90 kg)

dose = 0.0155 x 10-5 Sv/year

the total effective dose in rem/year for a 90-kg adult is given as ::

dose = (1.4 x 10-5 J/year) (1) / (1 x 10-2 J/kg-rad) (90 kg)

dose = 1.55 x 10-5 rem/yr

or   dose = 0.015 mrem/yr

(2) the total effective dose in Sv/year for a 8-kg baby is given as ::

dose = (1.4 x 10-5 J/year) (1) / (8 kg)

dose = 0.175 x 10-5 Sv/year

the total effective dose in rem/year for a 8-kg baby is given as ::

dose = (1.4 x 10-5 J/year) (1) / (1 x 10-2 J/kg-rad) (8 kg)

dose = 17.5 x 10-5 rem/yr

or   dose = 0.175 mrem/yr

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