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21. Nuclear Chemistry

Radioactive Half-Life

21. Nuclear Chemistry

Radioactive Half-Life

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Intro to Radioactive Half-Life

Intro to Radioactive Half-Life

Method 1 of Radioactive Half-Life

Method 1 of Radioactive Half-Life

Radioactive Half-Life Example

Radioactive Half-Life Example

Radioactive Half-Life Example

Radioactive Half-Life Example

Radioactive Half-Life Example

Radioactive Half-Life Example

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Practice this topic

Multiple Choice

The half-life of arsenic-74 is about 18 days. If a sample initially contains 5.13 x 10⁴ mg arsenic-74, what mass (in mg) would be left after 80 days?

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Multiple Choice

What percentage of carbon – 14 ( t_1/2 = 5715 years) remains in a sample estimated to be 18,315 years old?

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Textbook Question

Fluorine-18 undergoes positron emission with a half-life of 1.10 x 10^2 minutes. If a patient is given a 250 mg dose for a PET scan, how long will it take for the amount of fluorine-18 to drop to 75 mg? (a) 56 minutes (b) 96 minutes (c) 132 minutes (d) 191 minutes

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Textbook Question

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (b) What is the rate constant for the decay? [Section 21.4]

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Textbook Question

The accompanying graph illustrates the decay of 8842Mo, which decays via positron emission. (a) What is the halflife of the decay? [Section 21.4]

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Textbook Question

In a cave in Oregon, archaeologists found bones, plant remains, and fossilized feces. DNA remaining in the feces indi-cates their human origin but not their age. To date the remains, the decay rate was measured and found to be 2.71 disinte-grations/min per gram of carbon. Currently living organisms have a decay rate of 15.3 disintegrations/min per gram of carbon, and the half-life of 14C is 5715 years. How old are the remains? (a) 1460 years (b) 9900 years (c) 14300 years (d) 18600 years

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Textbook Question

Each statement that follows refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false. (a) If the half-life for A is shorter than the half-life for X, A has a larger decay rate constant.

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Textbook Question

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how much will a dial be dimmed in a watch that is 50 yr old?

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Textbook Question

Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity falls to 75% of the original sample. If an original sample was purchased in June 2016, when will it be necessary to replace the cobalt-60?

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Textbook Question

The cloth shroud from around a mummy is found to have a 14C activity of 9.7 disintegrations per minute per gram of carbon as compared with living organisms that undergo 16.3 disintegrations per minute per gram of carbon. From the half-life for 14C decay, 5715 yr, calculate the age of the shroud.

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Textbook Question

Potassium-40 decays to argon-40 with a half-life of 1.27 * 109 yr. What is the age of a rock in which the mass ratio of 40Ar to 40K is 4.2?

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Textbook Question

One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years. How long will it take for the amount of U-235 to reach 10.0% of its initial amount?

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Textbook Question

A radioactive sample contains 1.55 g of an isotope with a halflife of 3.8 days. What mass of the isotope remains after 5.5 days?

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Textbook Question

A sample of F-18 has an initial decay rate of 1.5 * 105>s. How long will it take for the decay rate to fall to 2.5 * 103>s? (F-18 has a half-life of 1.83 hours.)

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Textbook Question

The half-life of indium-111, a radioisotope used in studying the distribution of white blood cells, is t1/2 = 2.805 days. What is the decay constant of 111In?

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Textbook Question

The decay constant of plutonium-239, a waste product from nuclear reactors, is 2.88 * 10-5 year - 1. What is the half-life of 239Pu?

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Textbook Question

Polonium-209, an a emitter, has a half-life of 102 years. How many alpha particles are emitted in 1.0 s from a 1.0 ng sample of 209Po?

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Textbook Question

A mammoth skeleton has a carbon-14 decay rate of 0.48 disintegration per minute per gram of carbon (0.48 dis>min # g C). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis>min # g C and that carbon- 14 has a half-life of 5715 yr.)

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Textbook Question

A sample of 37Ar undergoes 8540 disintegrations/min initially but undergoes 6990 disintegrations/min after 10.0 days. What is the half-life of 37Ar in days?

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Textbook Question

Radioactive decay exhibits a first-order rate law, rate = -∆N/∆t = kN, where N denotes the number of radio-active nuclei present at time t. The half-life of strontium-90, a dangerous nuclear fission product, is 29 years. (a) What fraction of the strontium-90 remains after three half-lives?

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Textbook Question

Potassium ion, K+, is present in most foods and is an essen-tial nutrient in the human body. Potassium-40, however, which has a natural abundance of 0.0117%, is radioactive with t1/2 = 1.25 x 10^9 years. What is the decay constant of 40K? How many 40K+ ions are present in 1.00 g of KCl? How many disintegration/s does 1.00 g of KCl undergo?

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Textbook Question

Suppose a patient is given 1.55 mg of I-131, a beta emitter with a half-life of 8.0 days. Assuming that none of the I-131 is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?

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Textbook Question

The half-life of 238U is 4.5 * 109 yr. A sample of rock of mass 1.6 g produces 29 dis>s. Assuming all the radioactivity is due to 238U, find the percent by mass of 238U in the rock.

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Textbook Question

The half-life of 232Th is 1.4 * 1010 yr. Find the number of disintegrations per hour emitted by 1.0 mol of 232Th.

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Textbook Question

The maximum level of radon in drinking water is 4.0 pCi (4.0 x 10^-12Ci) per milliliter. (a) How many disintegrations occur per minute in 1 mL of water at the maximum radon level? (b) If the radioactive isotope is 222Rn(t1/2 = 3.8 days), how many 222Rn atoms are present in 1 mL of the water?

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Textbook Question

Nitrogen-16 is formed in the cooling water flowing through a hot reactor core in a nuclear power plant. It is formed when oxygen captures a neutron and then emits a b par-ticle. Determine the activity of 50.0 mg of 16N in units of Bq and Ci.

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What fraction of a reactant has been consumed after 4 half-lives in a first-order reaction?

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What is the rate constant of a first-order reaction when 20.0% of a reactant remains after 30.0 s?

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A fossil is found to have a ¹⁴C level of 76.0% compared to living organisms. How old is the fossil?

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A moon rock collected by the Apollo mission is estimated to be 3.80 billion years old by uranium/lead dating. Assuming that the rock did not contain any lead when it was formed, what is the current mass of 206 Pb in the rock, given that it currently contains 1.180 g of 238 u? The half-life of ²³⁸U is 4.47×10⁹ years.

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