21.3 Radioactive decay  (Page 9/21)

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

(a) ${}_{15}^{34}\text{P}$

(b) ${}_{92}^{239}\text{U}$

(c) ${}_{20}^{38}\text{Ca}$

(d) ${}_1^3\text{H}$

(e) ${}_{94}^{245}\text{Pu}$

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

(a) ${}_{15}^{28}\text{P}$

(b) ${}_{92}^{235}\text{U}$

(c) ${}_{20}^{37}\text{Ca}$

(d) ${}_3^9\text{L}\text{i}$

(e) ${}_{96}^{245}\text{Cm}$

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

(a) ${}_2^6\text{H}\text{e}$

(b) ${}_{30}^{60}\text{Zn}$

(c) ${}_{91}^{235}\text{Pa}$

(d) ${}_{94}^{241}\text{Np}$

(e) ¹⁸ F

(f) ¹²⁹ Ba

(g) ²³⁷ Pu

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

Write a nuclear reaction for each step in the formation of ${}_{82}^{208}\text{Pb}$ from ${}_{90}^{228}\text{T}\text{h,}$ 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.

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

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

(a) 5.0 min after it forms

(b) 1.0 h after it forms

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?

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?

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

The isotope ${}_{38}^{90}\text{Sr}$ 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.

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 ${}_{43}^{99}\text{Tc}.$

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

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 $\times$ 10 ¹⁰ y.

(b) If some ${}_{38}^{87}\text{Sr}$ 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 laboratory investigation shows that a sample of uranium ore contains 5.37 mg of ${}_{92}^{238}\text{U}$ and 2.52 mg of ${}_{82}^{206}\text{Pb}.$ Calculate the age of the ore. The half-life of ${}_{92}^{238}\text{U}$ is 4.5 $\times$ 10 ⁹ yr.

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 $\times$ 10 ⁹ years ago?

A ${}_4^7\text{Be}$ atom (mass = 7.0169 amu) decays into a ${}_3^7\text{L}\text{i}$ atom (mass = 7.0160 amu) by electron capture. How much energy (in millions of electron volts, MeV) is produced by this reaction?

A ${}_5^8\text{B}$ atom (mass = 8.0246 amu) decays into a ${}_4^8\text{B}$ 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?

Isotopes such as ²⁶ Al (half-life: 7.2 $\times$ 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 $\times$ 10 ⁹ (4.7 billion) years ago. How old was the earth when 99.999999% of the ²⁶ Al originally present had decayed?

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

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