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)

Answer 1

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 / t_1/2

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