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Ch 42: Nuclear Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 42: Nuclear PhysicsProblem 26c
Chapter 42, Problem 26c

Identify the unknown isotope XX in the following decays. 7Be+e−→X+ν^7\(\text{Be}\)+\(\text{e}\)^{-}\(\rightarrow\]\text{X}\)+\(\nu\)

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Understand the problem: The given reaction involves the decay of a beryllium-7 isotope (\( ^7\text{Be} \)) through electron capture. In this process, an electron (\( \text{e}^- \)) is captured by the nucleus, resulting in the formation of a new isotope (\( \text{X} \)) and the emission of a neutrino (\( \nu \)). The goal is to identify the unknown isotope \( \text{X} \).
Recall the concept of electron capture: During electron capture, a proton in the nucleus combines with an electron to form a neutron. This reduces the atomic number (\( Z \)) of the element by 1, while the mass number (\( A \)) remains unchanged because the total number of nucleons (protons + neutrons) is conserved.
Analyze the given isotope: \( ^7\text{Be} \) has an atomic number \( Z = 4 \) (beryllium) and a mass number \( A = 7 \). After electron capture, the atomic number decreases by 1, so the new atomic number becomes \( Z = 3 \). The mass number remains \( A = 7 \).
Identify the element with \( Z = 3 \): Using the periodic table, the element with atomic number \( Z = 3 \) is lithium (\( \text{Li} \)). Therefore, the unknown isotope \( \text{X} \) is \( ^7\text{Li} \).
Conclude: The reaction can now be written as \( ^7\text{Be} + \text{e}^- \rightarrow ^7\text{Li} + \nu \), where \( ^7\text{Li} \) is the identified isotope.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Isotopes

Isotopes are variants of a particular chemical element that have the same number of protons but different numbers of neutrons. This results in different atomic masses for the isotopes of the same element. Understanding isotopes is crucial in nuclear physics and chemistry, as they can exhibit different stability and decay properties, which are essential for identifying unknown isotopes in decay processes.

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or a positron) is emitted from an atomic nucleus. In the case of beta-minus decay, a neutron is transformed into a proton, emitting an electron and an antineutrino. This process is significant for understanding how isotopes transform into other elements or isotopes, which is central to solving the decay equation presented in the question.
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Conservation of Energy and Momentum

In nuclear reactions, the conservation of energy and momentum principles state that the total energy and momentum before the decay must equal the total energy and momentum after the decay. This principle is essential for analyzing decay processes, as it allows us to determine the properties of the unknown isotope by balancing the masses and energies involved in the decay equation.
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Related Practice
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A sample of 1.0 x 1010 atoms that decay by alpha emission has a half-life of 100 min. How many alpha particles are emitted between t = 50 min and t = 200 min?

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The radioactive isotope 230Th has a density of 11,700 kg/m3 and a half-life of 75,000 yr. What is the radius of a 230Th sphere that has an activity of 1.0 Ci?

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An unstable nucleus undergoes alpha decay with the release of 5.52 MeV of energy. The combined mass of the parent and daughter nuclei is 452 u. What was the mass number of the parent nucleus?

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Textbook Question

A Geiger counter is used to measure the decay of a radioactive isotope produced in a nuclear reactor. Initially, when the sample is first removed from the reactor, the Geiger counter registers 15,000 decays/s. 15 h later the count is down to 5500 decays/s. At what time after the sample's removal from the reactor is the count 1200 decays/s?

Textbook Question

For those that are not stable, identify both the decay mode and the daughter nucleus.

Textbook Question

Identify the unknown isotope XX in the following decays. X→40K+e++ν\(\text{X}\]\rightarrow\)^{40}\(\text{K}\)+\(\text{e}\)^{+}+\(\nu\)

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