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Chapter 42: Q 21 Exercise (page 1236)
The radioactive hydrogen isotope 3H, called tritium, has a
half-life of 12 years.
a. What are the decay mode and the daughter nucleus of tritium?
b. What are the lifetime and the decay rate of tritium?
Hence,
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What is the age in years of a bone in which the ratio is measured to be?
Consider a nucleus with mass number . Its mass, within , is atomic mass units.
The fact that cancels means that all nuclei have this density. It is a staggeringly large density, roughly times larger than the density of familiar liquids and solids.
One early objection to Rutherford’s model of a nuclear atom was that matter simply couldn’t have a density this high. Although we have no direct experience with such matter, nuclear matter really is this dense.
The rate at which a radioactive tracer is lost from a patient’s body is the rate at which the isotope decays plus the rate at which the element is excreted from the body. Medical experiments have shown that stable isotopes of a particular element are excreted with a 6.0 day half-life. A radioactive isotope of the same element has a half-life of 9.0 days. What is the effective half-life of the isotope, in days, in a patient’s body?
Stars are powered by nuclear reactions that fuse hydrogen into helium. The fate of many stars, once most of the hydrogen is used up, is to collapse, under gravitational pull, into a neutron star. The force of gravity becomes so large that protons and electrons are fused into neutrons in the reaction p+ + e- S n + n. The entire star is then a tightly packed ball of neutrons with the density of nuclear matter. a. Suppose the sun collapses into a neutron star. What will its radius be? Give your answer in km. b. The sun’s rotation period is now 27 days. What will its rotation period be after it collapses? Rapidly rotating neutron stars emit pulses of radio waves at the rotation frequency and are known as pulsars
You learned in Chapter 41 that the binding energy of the electron in a hydrogen atom is .
a. By how much does the mass decrease when a hydrogen atom is formed from a proton and an electron? Give your answer both in atomic mass units and as a percentage of the mass of the hydrogen atom.
b. By how much does the mass decrease when a helium nucleus is formed from two protons and two neutrons? Give your answer both in atomic mass units and as a percentage of the mass of the helium nucleus.
c. Compare your answers to parts a and b. Why do you hear it said that mass is “lost” in nuclear reactions but not in chemical reactions?
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