Iodine 131 is a radioactive material that decays according to the function A(t)=A0e-0.087(t) where A0 is the initial amount present, and A is the amount present at time (in days) Assume that a scientist has a sample of 200 grams of iodine 131.What is the decay rate of iodine 131?How much iodine 132 is left after 8 days?When will 70 grams of iodine 131 be left?What is the half-life of iodine 131?

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Asked Oct 24, 2019
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Iodine 131 is a radioactive material that decays according to the function A(t)=A0e-0.087(t) where A0 is the initial amount present, and A is the amount present at time (in days) Assume that a scientist has a sample of 200 grams of iodine 131.

  1. What is the decay rate of iodine 131?
  2. How much iodine 132 is left after 8 days?
  3. When will 70 grams of iodine 131 be left?
  4. What is the half-life of iodine 131? 
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Expert Answer

Step 1

Refer to the question . we have been given the iodine 131 which is a radioactive material that decays according to the function A(t)=A0e-0.087(t) . Here A0 represents the initial amount present and A is the amount present at time (in days). Also the sample is provided with 200 grams of iodine 131

A(t) 4e0870)
A (t) The amount present at time (in days)
A= Arepresents the initial amount
t=time in days
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A(t) 4e0870) A (t) The amount present at time (in days) A= Arepresents the initial amount t=time in days

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Step 2

(1)…To find the decay rate of iodine 131 compare the provided equation with the radioactive decay equation and from there we can find the decay rate as 0.087

N No6
= decay rate
so from A(t) = A e-0.07()
A = 0.087
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N No6 = decay rate so from A(t) = A e-0.07() A = 0.087

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Step 3

(2)…

As we can find the amount of iodine 131 and not 132 because we have not given the information about 132 ...

A (t) (200)e.0878)
0.087(8)
4(t) = 200e
1
- 200
S0.087
99.7151g
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A (t) (200)e.0878) 0.087(8) 4(t) = 200e 1 - 200 S0.087 99.7151g

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