Chapter 32, Problem 24PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# The annual radiation dose from 14C in our bodies is 0.01 mSv/y. Each 14C decay emits a β− averaging 0.0750 MeV. Taking the fraction of 14C to be 1.3 × 10 − 12 N of normal 12C, and assuming the body is 13% carbon, estimate the fraction of the decay energy absorbed. (The rest escapes, exposing those close to you.)

To determine

The fraction of the decay energy from 14C in our bodies, which is absorbed by our body.

Explanation

Given info:

The annual radiation dose from C14 in our bodies,

â€ƒâ€ƒdose=0.01Â mSv/y

Average energy of a Î²âˆ’ particle,

â€ƒâ€ƒEÎ²=0.0750Â MeV

Fraction of C14 atoms,

â€ƒâ€ƒN0=1.3Ã—10âˆ’12N of normal carbon

Percentage of carbon in a human body,

13%

Average mass of a human body,

â€ƒâ€ƒM=70.0Â kg

Half-life of C14 ,

â€ƒâ€ƒt1/2=5730Â y

Formula used:

The activity of a radioactive sample is given by,

â€ƒâ€ƒR=0.693N0t1/2

Here, N0 is the number of atoms of the radioactive substance present.

The dose in rem is related to the dose in rad as follows:

â€ƒâ€ƒdoseÂ inÂ rem=Â doseÂ inÂ radÃ—RBE

Here RBE is the relative biological effectiveness.

Calculation:

The radiation dose emitted by the human body is 0.01 mSv/y. Express the value in rem.

â€ƒâ€ƒdose=0.01Â mSv/yÃ—0.1Â rem1Â mSv=10âˆ’3rem/y

The RBE for Î² particle is 1.

Therefore,

Express the dose per year in J/kg.

The average mass of a human being is 70.0 kg. Assuming the radiation emitted is distributed uniformly in the body, the energy emitted in a year is given by,

â€ƒâ€ƒE=radiationÂ doseÃ—massÂ ofÂ theÂ human=10âˆ’5J/kgâ‹…yÃ—70.0Â kg=7.00Ã—10âˆ’4J/y

Express the energy in MeV/y.

â€ƒâ€ƒE=7.00Ã—10âˆ’4J/yÃ—1Â MeV1.6Ã— 10 âˆ’13J=4.375Ã—109MeV/y

The energy emitted by a human being in a year is therefore given by 4.375Ã—109MeV/y.

Given that mass of carbon in a human body is 13% of the mass, calculate the mass of carbon in the body.

â€ƒâ€ƒm=0

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