Potassium is a crucial element for the healthy operation of the human
body. Potassium occurs naturally in our environment (and thus our
bodies) as three isotopes: Potassium-39, Potassium-40, and Potassium-
41. Their current abundances are 93.26%, 0.012% and 6.728%. A typical
human body contains about 3.0 grams of Potassium per kilogram of body
mass.
1. How much Potassium-40 is present in a person with a mass of 80
kg?
2 If, on average, the decay of Potassium-40 results in 1.10 MeV of
energy absorbed, determine the effective dose (in Sieverts) per year
due to Potassium-40 in an 80-kg body. Assume an RBE of 1.2. The
half-life of Potassium-40 is 1.28 x 10° years.

1

  The mass of the Potassium-40 is  

2

  The Dose per year in Sieverts is  

Explanation:

From the question we are told that

   The isotopes of potassium in the body are Potassium-39, Potassium-40, and Potassium- 41

    Their abundance is 93.26%, 0.012% and 6.728%

   The mass of potassium contained in human body is   per kg of the body

    The mass of the first body is  

Now the mass of  potassium  in this body is mathematically evaluated as

substituting value

The amount of Potassium-40 present  is mathematically evaluated as

      0.012% * 0.024

The dose of energy absorbed per year is mathematically represented as

Where E is the energy absorbed which is given as

    Substituting value

The Dose in Sieverts is evaluated as

conservation of mass

mass before something happens = mass afterwards