/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 A nucleus of \(_{92}^{238} \math... [FREE SOLUTION] | 91Ó°ÊÓ

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A nucleus of \(_{92}^{238} \mathrm{U}\) captures a neutron to form an unstable nucleus that undergoes two successive beta minus decays. What is the resulting nucleus?

Short Answer

Expert verified
_{94}^{239} \mathrm{Pu}

Step by step solution

01

- Initial Neutron Capture

When \(_{92}^{238} \mathrm{U}\) captures a neutron, it becomes \(_{92}^{239} \mathrm{U}\). The captured neutron adds 1 to the mass number while the atomic number remains unchanged.
02

- First Beta Minus Decay

In a beta minus decay, a neutron is converted into a proton, and a beta particle (electron) and antineutrino are emitted. The atomic number increases by 1 while the mass number remains the same. Thus, \(_{92}^{239} \mathrm{U}\) decays to \(_{93}^{239} \mathrm{Np}\).
03

- Second Beta Minus Decay

Another beta minus decay occurs, increasing the atomic number by 1 again while the mass number remains unchanged. Consequently, \(_{93}^{239} \mathrm{Np}\) decays to \(_{94}^{239} \mathrm{Pu}\) (Plutonium-239).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

neutron capture
Neutron capture is a process where an atomic nucleus absorbs a neutron without releasing any particles. This happens often in nuclear reactions, especially within reactors and stars. In this exercise, Uranium-238 (\(_{92}^{238} \mathrm{U}\)) captures a neutron, transforming into Uranium-239 (\

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