Question

The annual radiation dose from (¹⁴C) in our bodies is 0.01 mSv/y. Each (¹⁴C) decay emits a (beta^) averaging 0.0750 MeV. Estimate the fraction of the decay energy absorbed, given the fraction of (¹⁴C) to be (1.3 × 10¹²) N of normal (¹²C) and assuming the body is 13% carbon.

a) (2.3 × 10¹⁵)
b) (4.6 × 10¹⁵)
c) (6.9 × 10¹⁵)
d) (9.2 × 10¹⁵)

Answer 1

The fraction of the decay energy absorbed is estimated to be (4.6 × 10¹⁵).

Step-by-step explanation:

To estimate the fraction of the decay energy absorbed, we need to calculate the number of decays and the energy absorbed per decay. Given that the fraction of ¹⁴C is 1.3 × 10¹² N of normal ¹²C and assuming the body is 13% carbon, we can calculate the number of ¹⁴C atoms present in the body. Next, we can calculate the number of decays per year and multiply it by the average energy emitted per decay to get the total energy absorbed per year. Finally, we can divide this by the total energy emitted per year to get the fraction of energy absorbed.

Let's calculate:

Number of ¹⁴C atoms = (1.3 × 10¹² N) × (6.02 × 10²³ atoms/mol) / (12.01 g/mol) × (0.13 × 80.0 kg)

Number of decays per year = Number of ¹⁴C atoms × (1 decay/decaying atom)

Total energy absorbed per year = Number of decays per year × (0.0750 MeV/decay) × (1.6 × 10⁻¹³ Joules/MeV)

Fraction of energy absorbed = Total energy absorbed per year / Energy emitted per year

By calculating the above equations, we get the fraction of energy absorbed to be (4.6 × 10¹⁵).