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The following nuclei do not lie in the band of stability. How would they be expected to decay? Explain your answer.

(a) 15 34 P

(b) 92 239 U

(c) 20 38 Ca

(d) 1 3 H

(e) 94 245 Pu

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The following nuclei do not lie in the band of stability. How would they be expected to decay?

(a) 15 28 P

(b) 92 235 U

(c) 20 37 Ca

(d) 3 9 L i

(e) 96 245 Cm

(a) β decay; (b) α decay; (c) positron emission; (d) β decay; (e) α decay

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Predict by what mode(s) of spontaneous radioactive decay each of the following unstable isotopes might proceed:

(a) 2 6 H e

(b) 30 60 Zn

(c) 91 235 Pa

(d) 94 241 Np

(e) 18 F

(f) 129 Ba

(g) 237 Pu

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Write a nuclear reaction for each step in the formation of 84 218 Po from 98 238 U , which proceeds by a series of decay reactions involving the step-wise emission of α, β, β, α, α, α particles, in that order.

92 238 U 90 234 Th + 2 4 He ; 90 234 Th 91 234 Pa + -1 0 e ; 91 234 Pa 92 234 U + -1 0 e ; 92 234 U 90 230 Th + 2 4 He 90 230 Th 88 226 Ra + 2 4 He 88 226 Ra 86 222 Rn + 2 4 He ; 86 222 Rn 84 218 Po + 2 4 He

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Write a nuclear reaction for each step in the formation of 82 208 Pb from 90 228 T h, which proceeds by a series of decay reactions involving the step-wise emission of α, α, α, α, β, β, α particles, in that order.

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Define the term half-life and illustrate it with an example.

Half-life is the time required for half the atoms in a sample to decay. Example (answers may vary): For C-14, the half-life is 5770 years. A 10-g sample of C-14 would contain 5 g of C-14 after 5770 years; a 0.20-g sample of C-14 would contain 0.10 g after 5770 years.

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A 1.00 × 10 –6 -g sample of nobelium, 102 254 No , has a half-life of 55 seconds after it is formed. What is the percentage of 102 254 No remaining at the following times?

(a) 5.0 min after it forms

(b) 1.0 h after it forms

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239 Pu is a nuclear waste byproduct with a half-life of 24,000 y. What fraction of the 239 Pu present today will be present in 1000 y?

( 1 2 ) 0.04 = 0.973 or 97.3%

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The isotope 208 Tl undergoes β decay with a half-life of 3.1 min.

(a) What isotope is produced by the decay?

(b) How long will it take for 99.0% of a sample of pure 208 Tl to decay?

(c) What percentage of a sample of pure 208 Tl remains un-decayed after 1.0 h?

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If 1.000 g of 88 226 Ra produces 0.0001 mL of the gas 86 222 Rn at STP (standard temperature and pressure) in 24 h, what is the half-life of 226 Ra in years?

2 × 10 3 y

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The isotope 38 90 Sr is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample diminishes to 0.393 g in 10.0 y. Calculate the half-life.

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Technetium-99 is often used for assessing heart, liver, and lung damage because certain technetium compounds are absorbed by damaged tissues. It has a half-life of 6.0 h. Calculate the rate constant for the decay of 43 99 Tc .

0.12 h –1

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What is the age of mummified primate skin that contains 8.25% of the original quantity of 14 C?

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A sample of rock was found to contain 8.23 mg of rubidium-87 and 0.47 mg of strontium-87.

(a) Calculate the age of the rock if the half-life of the decay of rubidium by β emission is 4.7 × 10 10 y.

(b) If some 38 87 Sr was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in (a)? Explain your answer.

(a) 3.8 billion years;
(b) The rock would be younger than the age calculated in part (a). If Sr was originally in the rock, the amount produced by radioactive decay would equal the present amount minus the initial amount. As this amount would be smaller than the amount used to calculate the age of the rock and the age is proportional to the amount of Sr, the rock would be younger.

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A laboratory investigation shows that a sample of uranium ore contains 5.37 mg of 92 238 U and 2.52 mg of 82 206 Pb . Calculate the age of the ore. The half-life of 92 238 U is 4.5 × 10 9 yr.

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Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in 1941. They proposed that the source of this 239 Pu was the capture of neutrons by 238 U nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7 × 10 9 years ago?

c = 0; This shows that no Pu-239 could remain since the formation of the earth. Consequently, the plutonium now present could not have been formed with the uranium.

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A 4 7 Be atom (mass = 7.0169 amu) decays into a 3 7 L i atom (mass = 7.0160 amu) by electron capture. How much energy (in millions of electron volts, MeV) is produced by this reaction?

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A 5 8 B atom (mass = 8.0246 amu) decays into a 4 8 B atom (mass = 8.0053 amu) by loss of a β + particle (mass = 0.00055 amu) or by electron capture. How much energy (in millions of electron volts) is produced by this reaction?

17.5 MeV

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Isotopes such as 26 Al (half-life: 7.2 × 10 5 years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclides.

(a) 26 Al decays by β + emission or electron capture. Write the equations for these two nuclear transformations.

(b) The earth was formed about 4.7 × 10 9 (4.7 billion) years ago. How old was the earth when 99.999999% of the 26 Al originally present had decayed?

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Write a balanced equation for each of the following nuclear reactions:

(a) bismuth-212 decays into polonium-212

(b) beryllium-8 and a positron are produced by the decay of an unstable nucleus

(c) neptunium-239 forms from the reaction of uranium-238 with a neutron and then spontaneously converts into plutonium-239

(d) strontium-90 decays into yttrium-90

(a) 83 212 Bi 84 212 Po + -1 0 e ; (b) 5 8 B 4 8 B e + -1 0 e ; (c) 92 238 U + 0 1 n 93 239 Np + -1 0 N p , 93 239 Np 94 239 Pu + -1 0 e ; (d) 38 90 Sr 39 90 Y + -1 0 e

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Write a balanced equation for each of the following nuclear reactions:

(a) mercury-180 decays into platinum-176

(b) zirconium-90 and an electron are produced by the decay of an unstable nucleus

(c) thorium-232 decays and produces an alpha particle and a radium-228 nucleus, which decays into actinium-228 by beta decay

(d) neon-19 decays into fluorine-19

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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