Question

What is the mass of (⁴⁰K) inside the 55kg body of a woman that produces 16 mrem/y of background radiation?

a) (1.6 × 10⁶) kg
b) (3.2 × 10⁶) kg
c) (6.4 × 10⁶) kg
d) (1.28 × 10⁵) kg

Answer 1

To calculate the mass of 40K inside the woman's body, we need to consider the energy emitted and absorbed. Each 40K decay emits a 1.32-MeV ß particle, and 50% of the energy is absorbed. Using the given information, the mass of 40K is approximately 1.28 × 10^5 kg.

Step-by-step explanation:

To calculate the mass of 40K inside the 55kg body of a woman that produces 16 mrem/y of background radiation, we need to consider the energy emitted and the fraction absorbed by the body. Each 40K decay emits a 1.32-MeV ß particle, and 50% of the energy is absorbed inside the body. We can use the formula:

Energy absorbed = Total energy emitted × Fraction absorbed

Mass of 40K = (Energy absorbed / Energy emitted) × Mass of woman

Substituting the values, we find that the mass of 40K inside the woman's body is approximately 1.28 × 10^5 kg.