3.36 On March 11, 2011, a massive earthquake and tsunami triggered a major disas
ID: 887831 • Letter: 3
Question
3.36
On March 11, 2011, a massive earthquake and tsunami triggered a major disaster at Japan’s
Fukushima nuclear plant. A plume extending to the northwest of the site deposited significant amounts of iodine-131, cesium-134, and cesium-137 up to 30 miles away. Iodine-131 has an 8-day half-life and cesium-137 has a 3-year half-life. Determine how long it will take 99% of the iodine-131 and 99% of the cesium-
137 to naturally decay (you can learn about “U.S. Nuclear Power Safety One Year after Fukushima” by readin
g the report written by D. Lochbaum and E. Lyman, located on the web site of the Union of Concerned Scientists, http://www.ucsusa.org/publications/publications-nuclear-power.html)
Explanation / Answer
Solution :-
Half life of 131 I = 8 days
Half life of the 134 Cs =3 year
Lets first calculate the rate constants for the both
K= 0.693 / t1/2
Rate constant for iodine = 0.693 / 8 day = 0.086625 day-1
Rate constant for the Cs = 0.693 / 3 years = 0.231 yr-1
Now lets calculate the time needed to decay 99% of the original sample of both using the first order rate equation
Assume initial concentration is 100 % and then final concentration is 100%-99% = 1 %
Calculating time needed for the decay of the iodine
ln ([A]t/[A]o)= -K*t
where [A]t = final cocnetration and [A]o = initial concentration , t= time and k = rate constant
lets put the values in the formula
ln(1/100) = -0.086625 day-1 * t
-4.605 = -0.086625 day-1 * t
-4.605 / -0.086625 day-1 = t
53.2 days = t
Therefore time needed for the decay of the 131 iodine is 53.2 days
Now lets calculate the time needed for the 134Cs
ln ([A]t/[A]o)= -K*t
ln(1/100) = -0.231 yr-1 * t
-4.605 = -0.231 yr-1 *t
-4.605 / -0.231 yr-1 = t
19.9 yr = t
Therefore time needed for the 99% decay of the 134Cs is 19.9 year or we can round it to 20.0 year
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