After the Chernobyl disaster, radioactive isotopes were released into the environment. One such isotope was Cesium-137. The town nearest to the Chernobyl power plant is Pripyat. After the disaster, the activity from the radioactive decay of Cesium-137 was measured to be [tex]1 \times 10^{13}[/tex] decays/sec. Cesium-137 decays into Barium-137 by beta decay. The electrons emitted by the radioactive decay of Cesium-137 have an energy of 1.17 MeV. The molar mass of Cesium-137 is 136.91 g/mol, the half-life of Cesium-137 is 30.2 years, and Avogadro's number is [tex]6.022 \times 10^{23}[/tex] particles/mole. The RBE factor of these electrons is 1. The number of seconds in a year is [tex]3.154 \times 10^{7}[/tex] sec.

(a) What is the initial mass of Cesium-137 that was released into the environment in Pripyat?

(b) How long will it take for the activity to drop to a much safer level of 10 decays/sec in Pripyat?

For parts (c) and (d), we will consider a person with a mass of 80 kg, referred to as Person 1. Let's say that Person 1 remained outside in Pripyat for 2 days (172,800 sec) after the Chernobyl disaster, with no protection from the radiation.

(c) What is the absorbed dose received by Person 1, 2 days after the Chernobyl disaster, from the radioactive decay of Cesium-137?

(d) Did Person 1 from part (c) receive a lethal dose in these 2 days? A lethal dose is about [tex]1 \times 10^{9}[/tex] J/kg.

For parts (e) and (f), we will consider a person with a mass of 80 kg, referred to as Person 2. Let's say that Person 2 remained outside in Pripyat for 1 year after the Chernobyl disaster, with no protection from the radiation.

(e) What is the equivalent dose received by Person 2, 1 year after the Chernobyl disaster, from the radioactive decay of Cesium-137?

(f) Define your answer from part (e) as ED_Cesium. The maximum allowed radiation level for a radiation worker in a year is [tex]ED_{safe} = 0.02[/tex] Sv. What is the value of the ratio [tex]ED_{Cesium}/ED_{safe}[/tex]? This number will tell us how many times larger the equivalent dose from part (e) is compared to a safe equivalent dose.

The activity of Cesium-137 is given as 1 x 10¹³ decays/sec. Mass of Cesium-137 released can be calculated by first using the formula for the decay constant λ λ = ln2/T₁/₂where T₁/₂ is the half life of Cesium-137

Substituting the values in the above equation λ = ln2/30.2 = 0.0229 yr⁻¹

Then, using the formula for activity A = λN

where N is the number of particles A = λN1 x 10¹³ = 0.0229 x N

⇒ N = 4.36 x 10²³

The mass of Cesium-137 can be calculated as Mass = Number of particles x Molar mass

Mass = 4.36 x 10²³ x 136.91 g/mol = 5.98 x 10²⁵ g

The activity of Cesium-137 drops with time and can be calculated as A = A₀ e^(-λt)where A₀ is the initial activity, λ is the decay constant and t is the time A₀ = 1 x 10¹³ decays/secλ = 0.0229 yr⁻¹A = 10 decays/sec

Substituting the values in the above equation10 = 1 x 10¹³ e^(-0.0229 t)

⇒ t = 207.8 years

Absorbed dose is given by the formula D = RBE x A x t / m where RBE is the relative biological effectiveness, A is the activity, t is the time, m is the mass of the person D = 1 x 1.17 x 10⁶ x 172800 / 80 = 3.14 x 10¹² J/kg(d) Lethal dose is given as 1 x 10⁹ J/kg. The dose received by Person 1 is much greater than the lethal dose, so Person 1 would have received a lethal dose.(e) Equivalent dose is given as H = D x Q where D is the absorbed dose, Q is the quality factor for beta particles which is 1H = 3.14 x 10¹² x 1 = 3.14 x 10¹² J/kg(f) Maximum allowed radiation level is ED safe = 0.02 Sv ED Cesium/ED safe = H Cesium/ H safe ED Cesium/ED safe = 3.14 x 10¹² / 0.02ED Cesium/ED safe = 1.57 x 10¹⁴This number tells us that the equivalent dose from the radioactive decay of Cesium-137 is 1.57 x 10¹⁴ times larger than a safe equivalent dose.

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