Question

Potassium is a crucial element for the healthy operation of the human

Answer 1

Answer:

1

  The mass of the Potassium-40 is  $m_{40}} = 2.88*10^{-6} kg$

2

  The Dose per year in Sieverts is   $Dose_s = 26.4 *10^{-10}$

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  $m = 3.0 g = \frac{3}{1000} = 0.0003 \ kg$ per kg of the body

    The mass of the first body is  $m_1 = 80 \ kg$

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

       $m_p = m * m_1$

substituting value

       $m_p = 80 * 0.0003$

      $m_p =0.024 kg$

The amount of Potassium-40 present  is mathematically evaluated as

      $m_{40}} =$0.012% * 0.024

      $m_{40}} = \frac{0.012}{100} * 0.024$

      $m_{40}} = 2.88*10^{-6} kg$

The dose of energy absorbed per year is mathematically represented as

          $Dose = \frac{E}{m_1}$

Where E is the energy absorbed which is given as $E = 1.10 MeV = 1.10 * 10^6 * 1.602*10^{-19}$

    Substituting value

            $Dose = \frac{ 1.10 * 10^6 * 1.602*10^{-19}}{80}$

            $Dose = 22*10^{-10} J/kg$

The Dose in Sieverts is evaluated as

       $Dose_s = REB * Dose$

       $Dose_s = 1.2 * 22*10^{-10}$

       $Dose_s = 26.4 *10^{-10}$