On April 26, 1986, an explosion at the nuclear power plant at Chernobyl, Ukraine, released the greatest quantity of radioactive material ever associated with an industrial accident. (See the discussion and photo on pages 1131-1132.) One of the radioisotopes in this emission was ^131I, a β^- emitter

Question

On April 26, 1986, an explosion at the nuclear power plant at Chernobyl, Ukraine, released the greatest quantity of radioactive material ever associated with an industrial accident. (See the discussion and photo on pages 1131-1132.) One of the radioisotopes in this emission was [latex]_{}^{131} ext{I}[/latex], a [latex]\beta^-[/latex] emitter with a half-life of 8.04 days.
Assume that the total quantity of [latex]_{}^{131} ext{I}[/latex] released was 250 g, and determine the number of curies associated with this [latex]_{}^{131} ext{I}[/latex] 30.0 days after the accident.

Analyze
From the initial mass of [latex]_{}^{131} ext{I}[/latex] and the known half-life of [latex]_{}^{131} ext{I}[/latex] determine how many grams of [latex]_{}^{131} ext{I}[/latex] remain after 30 days. Convert this mass to a number of atoms using the molar mass of [latex]_{}^{131} ext{I}[/latex] and Avogadro's number. Finally, the product of the number of atoms and the decay constant yields the activity in disintegrations per second, which can be converted to curies.

Accepted Answer

In equation (25.12), use λ = 0.693/8.04 d and t = 30.0 d. Because the mass of [latex]_{}^{131} ext{I}[/latex] is directly proportional to the number of [latex]_{}^{131} ext{I}[/latex] atoms, we can replace [latex]N_0[/latex] by [latex]{mass}_0 = 250 g[/latex], and [latex]N_t[/latex] by [latex]{mass}_t[/latex], the mass we seek.

[latex]\ln \left(\frac{N_t}{N_0} ight)=-\lambda t[/latex] (25.12)

[latex]\ln \frac{ ext {mass}_t}{{mass}_0}=\ln \frac{{mass}_t}{250 g } = \frac{-0.693}{8.04 d } imes 30.0 d =-2.59[/latex]

[latex] ext {mass}_t = 250 g imes e ^{-2.59} = 250 g imes 0.0750 = 18.8 g[/latex]

To determine the number of iodine-131 atoms, use the molar mass, 131 g [latex]_{}^{131} ext{I}[/latex]/mol [latex]_{}^{131} ext{I}[/latex], and the Avogadro constant.

[latex]N_t = 18.8 g ext{ } _{}^{131} ext{I} imes \frac{1 mol ext{ } _{}^{131} ext{I} }{131 g ext{ } _{}^{131} ext{I} } imes \frac{6.022 imes 10^{23} ext{ } _{}^{131} ext{I} ext { atoms }}{1 mol ext{ } _{}^{131} ext{I} }[/latex]

[latex]=8.64 imes 10^{22} ext{ } _{}^{131} ext{I} ext { atoms }[/latex]

To establish the decay constant in [latex]s^{-1}[/latex] and to obtain λ from [latex]t_{1/2}[/latex], use the method outlined in Example 25-3a.

[latex]\lambda = 0.693 / t_{1 / 2}=\frac{0.693}{8.04 d } imes \frac{1 d }{24 h } imes \frac{1 h }{60 min } imes \frac{1 min }{60 s }[/latex]

[latex]=9.98 imes 10^{-7} s ^{-1}[/latex]

To determine the decay rate (activity) after 30.0 days, use the two previous results in equation (25.11).

rate of decay ∝ N and rate of decay = A = λN (25.11)

[latex]A=\lambda N = 9.98 imes 10^{-7} s ^{-1} imes 8.64 imes 10^{22} ext { atoms }[/latex]

[latex]=8.62 imes 10^{16} ext{ dis } s ^{-1}[/latex]

Finally, to express the activity in curies use the definition of a curie given in Table 25.4.

[latex]A = 8.62 imes 10^{16} ext{ dis } s ^{-1} imes \frac{1 Ci }{3.70 imes 10^{10} ext{ dis } s ^{-1}}[/latex]

[latex]= 2.33 imes 10^6 Ci[/latex]

Assess
In this calculation we could also have shown that in 30 days (about [latex]4 imes t_{1/2}[/latex]) approximately 93% of the [latex]_{}^{131} ext{I}[/latex] had disintegrated. In the process, approximately [latex]2 imes 10^6[/latex] Ci of radiation was emitted. If we also knew the energy of the [latex]\beta^-[/latex] particles and something about the exposed population, we could also have estimated radiation doses in rads.

Question 25.Int.1: On April 26, 1986, an explosion at the nuclear power plant a...

Related Answered Questions

Verified Answer:

Verified Answer:

Verified Answer:

Predicting Which Nuclei Are Radioactive Which of the following nuclides would you expect to be stable, and which radioactive? (a) ^82As; (b) ^118Sn; (c) ^214Po. Analyze This question requires us to apply the rules of nuclear stability. We may also use Figure 25-7 to determine whether the nuclide ...

Verified Answer:

Applying the Integrated Rate Law for Radioactive Decay: Radiocarbon Dating A wooden object found in an Indian burial mound is subjected to radiocarbon dating. The activity associated with its ^14C content is 10 dis min^-1 g^-1. What is the age of the object? In other words, how much time has ...

Verified Answer:

Verified Answer: