21.3 Radioactive Decay

What are the types of radiation emitted by the nuclei of radioactive elements?

What is the change in the nucleus that results from the following decay scenarios?

(a) emission of a β particle

(b) emission of a β⁺ particle

(c) capture of an electron

Why is electron capture accompanied by the emission of an X-ray?

Which of the following nuclei is most likely to decay by positron emission? Explain your choice.

(a) chromium-53

(b) manganese-51

(c) iron-59

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

Write a nuclear reaction for each step in the formation of $_{ 84}^{218} \text{Po}$ from $_{ 92}^{238} \text{U} ,$ which proceeds by a series of decay reactions involving the step-wise emission of α, β, β, α, α, α, α particles, in that order.

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

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

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 ²²⁶Ra in years?

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

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 $\times$ 10¹⁰ 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.

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 ²³⁹Pu was the capture of neutrons by ²³⁸U nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7 $\times$ 10⁹ years ago?

A $_{5}^{8} \text{B}$ atom (mass = 8.0246 amu) decays into a $_{4}^{8} \text{Be}$ 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?

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