Skip to main content
Ch 42: Nuclear Physics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 42: Nuclear PhysicsProblema 27c
Capitolo 42, Problema 27c

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

Guida verificata passo dopo passo
1
Understand the problem: The given decay involves an unknown isotope (X) decaying into potassium-40 (40K), a positron (e+), and a neutrino (ν). This is a beta-plus (β+) decay, where a proton in the nucleus of the parent isotope is converted into a neutron, emitting a positron and a neutrino.
Apply the principle of conservation of nucleon number: The total number of nucleons (protons + neutrons) must remain the same before and after the decay. Since 40K has a mass number of 40, the unknown isotope X must also have a mass number of 40.
Apply the principle of conservation of charge: In β+ decay, the atomic number of the daughter nucleus decreases by 1 because a proton is converted into a neutron. Potassium (K) has an atomic number of 19, so the unknown isotope X must have an atomic number of 20 (19 + 1).
Identify the element with atomic number 20: Using the periodic table, the element with atomic number 20 is calcium (Ca). Therefore, the unknown isotope is calcium-40 (40Ca).
Summarize the result: The unknown isotope X is identified as calcium-40 (40Ca), which undergoes β+ decay to produce potassium-40 (40K), a positron, and a neutrino.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

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, as they can undergo various types of decay, affecting their stability and the reactions they participate in.

Beta Plus Decay

Beta plus decay is a type of radioactive decay in which a proton in the nucleus of an atom is transformed into a neutron, emitting a positron (e+) and a neutrino (ν) in the process. This decay decreases the atomic number of the element by one while keeping the mass number constant. Recognizing this decay process is essential for identifying the parent isotope and the resulting daughter isotope.
Video consigliato:
Percorso guidato
04:24
Amplitude Decay in an LRC Circuit

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 helps in analyzing decay processes and determining the properties of the emitted particles, such as the positron and neutrino in beta plus decay, ensuring that the reaction adheres to fundamental physical laws.
Video consigliato:
Percorso guidato
05:58
Conservation Of Momentum
Pratica correlata
Domanda del libro di testo

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?

63
views
Domanda del libro di testo

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?

53
views
Domanda del libro di testo

What is the total energy (in MeV) released in the beta-minus decay of ³H?

67
views
Domanda del libro di testo

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?

65
views
Domanda del libro di testo

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

48
views
Domanda del libro di testo

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

71
views