Chapter 42, Problem 080 Because of the 1986 explosion and fire in a reactor at t

Question

Chapter 42, Problem 080 Because of the 1986 explosion and fire in a reactor at the Chernobyl nuclear power plant in northern Ukraine, part of Ukraine is contaminated with 137Cs, which undergoes beta-minus decay with a haif-life of 30.2 y. In 1996, the total activity of this contamination over an area of 2.6 x 105 km2 was estimated to be 1 x 1016 Bq. Assume that the 137Cs is uniformly spread over that area and that the beta-decay electrons travel either directly upward or directly downward. How many beta-decay electrons would as 1 m2)Pr you you intercept were you to lie on the ground in that area for 1 h (a) in 1996 and (b) 2002? (You need to estimate your cross-sectional area that intercepts those electrons as 1 m2.) (a) Number (b) Number Show Work is REQUIRED for this question: Units Units Open Show Work

Explanation / Answer

Considering that i am 1.9m tall and .6 m broad , my cross sectional area that will be exposed would be

A = 1.9* .6 = 1.14 m^2

Hence the number of electrons crossing me will be

N = cross section/ total area * activity * time

N= 1.14/2.6*10^11 * 10^16 *60/2 = 1.31 *10^6 electrons

After 6 year the activity will change as

A = lambda N ; Ae-ln2 t/t1/2

A = 10^16 e^(-ln2 t/t1/2  ) = 0.41 *10^16

Hence the number will be reduced to 0.53 *10^6 electrons

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