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Ch.21 - Nuclear Chemistry
Chapter 21, Problem 5d

The steps below show three of the steps in the radioactive decay chain for 23290Th. The half-life of each isotope is shown below the symbol of the isotope. (d) The next step in the decay chain is an alpha emission. What is the next isotope in the chain? [Sections 21.2 and 21.4]

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1
Identify the type of decay mentioned in the problem, which is alpha emission. Alpha emission involves the release of an alpha particle from the nucleus, which consists of 2 protons and 2 neutrons.
Determine the change in atomic number and mass number due to the alpha emission. The atomic number decreases by 2 and the mass number decreases by 4 because an alpha particle (which is a helium nucleus, <sup>4</sup><sub>2</sub>He) is emitted.
Write the general equation for alpha decay: <sup>A</sup><sub>Z</sub>X -> <sup>A-4</sup><sub>Z-2</sub>Y + <sup>4</sup><sub>2</sub>He, where X is the parent isotope and Y is the daughter isotope.
Apply the alpha decay equation to the given isotope, <sup>232</sup><sub>90</sub>Th. Substitute A = 232 and Z = 90 into the equation to find the new isotope: <sup>232-4</sup><sub>90-2</sub>Y = <sup>228</sup><sub>88</sub>Y.
Identify the element with atomic number 88, which is Radium (Ra). Therefore, the next isotope in the decay chain after alpha emission from <sup>232</sup><sub>90</sub>Th is <sup>228</sup><sub>88</sub>Ra.

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Key Concepts

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

Radioactive Decay

Radioactive decay is the process by which an unstable atomic nucleus loses energy by emitting radiation. This can occur in various forms, including alpha, beta, and gamma decay. Each type of decay results in the transformation of the original isotope into a different element or isotope, characterized by a specific half-life, which is the time required for half of the radioactive atoms in a sample to decay.
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Rate of Radioactive Decay

Alpha Emission

Alpha emission is a type of radioactive decay in which an atomic nucleus releases an alpha particle, consisting of two protons and two neutrons. This process decreases the atomic number of the original isotope by two and the mass number by four, resulting in the formation of a new element. Understanding alpha emission is crucial for predicting the next isotope in a decay chain.
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Decay Chain

A decay chain, or radioactive series, is a sequence of decays that a radioactive isotope undergoes until it reaches a stable isotope. Each step in the chain involves the transformation of one isotope into another, often through various types of decay. The identification of the next isotope in a decay chain requires knowledge of the initial isotope and the type of decay occurring at each step.
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