Half life information that is available is reference to info available onine. *T

Question

Half life information that is available is reference to info available onine. *This is the entire problem*

The accident at Fukushima started with a tsunami on 3/11/2014. Most of the rest of the reactor issues developed over the course of just a few days afterward, so we can use 3/11/2014 as the reference date for these calculations. Use the half-life information that is available to compute the fractions (let's call it A/A_o where A = the radioactivity of some isotope) remaining today for the emitted^131 l, ^137 Cs, and^90 Sr. Compute the number of years required for all of these to decay to 0.1% of the emitted amount.

Explanation / Answer

1.a. The half-life for each of the isotopes is (source: http://www.periodictable.com/Isotopes/055.137/):

131I = 8.021 days

137Cs = 30.187 years

90Sr = 28.808 years

We need to calculate k (the rate constant) for each element using its half-life time and the formula:

k = ln2/t1/2

Where k = rate constant and t1/2 = half-life time

For 131I

k = ln2/8.021days

k = 0.086416554 days-1

For 137Cs

k = ln2/30.187 years

k = 0.022961777 years-1

For 90Sr

k = ln2/28.808 years

k = 0.024060926 years-1

Now, with the rate constant for each isotope-decay we can use the formula:

A = A0e-kt

Where A = remaining isotope, A0 = initial isotope, k = rate constant, t = time elapsed.

Before we move on we need to calculate the time, considering the reaction started on 3/11/2014 and that today is 5/25/2017, there have been 1171 days (3.208219178 years).

So, to calculate the remaining fractions of each isotope we'll use the formula above and the time in days or years between 3/11/2014 and today. We'll also consider A0 = 1 to make our calculations easier.

For 131I

A = e-kt

A = e-(0.086416554 days-1)(1171 days)

A = 1.127 x 10-44

For 137Cs

A = e-kt

A = e-0.022961777 years-1(3.208219178 years)

A = 0.9290

For 90Sr

A = e-kt

A = e-(0.024060926 years-1)(3.208219178 years)

A = 0.9257

1.b. We'll use the same formulas but we'll substitute A = 0.01 (because 0.01 is the 0.1% of 1), A0 = 1 and we'll use the same k for each isotope:

0.01 = e-kt

Solving for t

ln0.01 = -kt

t = -ln0.01/k

For 131I

t = -ln0.01/k

t = -ln0.01/0.086416554 days-1

t = 53.29 days or 0.146 years

For 137Cs

t = -ln0.01/k

t = -ln0.01/0.022961777 years-1

t = 200.56 years

For 90Sr

t = -ln0.01/k

t = -ln0.01/0.024060926 years-1

t = 191.40 years

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.