Calculate the effective radiation dosage in sieverts for a 57 57 ‑kg person who is exposed to 4.2 × 10 9 4.2×109 particles of alpha radiation. Only 81 % 81% of the radiation is absorbed. Assume each alpha particle has an energy of 6.1 × 10 − 13 6.1×10−13 J and that the RBE of the alpha particles is 15 15 . Note that RBE is sometimes called the quality factor ( Q Q ).

  Dose = 5.4 10⁻⁴  Sv

Explanation:

The radiation dose absorbed by the body is 81% of the incident radiation, which is the number of particles per energy of each particle

    E = 0.81 n₀ E₀

    E = 0.81 4.2 10⁹ 0.81 6.1 10⁻¹³

    E = 2.075 10⁻³ J

Effective radiation dose

     Dose1 = n x RBE

     Dose1 = 2,075 10⁻³ 15

     Dose1 = 3.1 10⁻² REM

The effective radiation dose in sievert

          Dose = dose1 / m

          Dose = 3.1 10⁻² / 57

          Dose = 5.4 10⁻⁴      [j / kg]

          Dose = 5.4 10⁻⁴  Sv