Write a partial decay series for Th-232 undergoing the sequential decays: a, b, b, a.

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insert step 1> Identify the initial isotope: Thorium-232 (\(^{232}_{90}\text{Th}\)).

insert step 2> Apply the first decay: Alpha decay reduces the atomic number by 2 and the mass number by 4. The new isotope is \(^{228}_{88}\text{Ra}\).

insert step 3> Apply the second decay: Beta decay increases the atomic number by 1 and keeps the mass number the same. The new isotope is \(^{228}_{89}\text{Ac}\).

insert step 4> Apply the third decay: Another beta decay increases the atomic number by 1 again, resulting in \(^{228}_{90}\text{Th}\).

insert step 5> Apply the fourth decay: Another alpha decay reduces the atomic number by 2 and the mass number by 4, resulting in \(^{224}_{88}\text{Ra}\).

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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 unstable atomic nuclei lose energy by emitting radiation. This can occur in various forms, including alpha (α) decay, where a helium nucleus is emitted, and beta (β) decay, where a neutron is transformed into a proton, emitting an electron. Understanding these decay processes is essential for predicting the behavior of radioactive isotopes over time.

Decay Series

A decay series is a sequence of radioactive decays that an unstable isotope undergoes until it reaches a stable end product. Each step in the series involves the transformation of one element into another, often through multiple decay processes. For Th-232, the decay series illustrates how it transforms through various isotopes until it stabilizes, which is crucial for understanding its long-term behavior in nature.

Alpha and Beta Decay

Alpha decay involves the emission of an alpha particle (two protons and two neutrons), resulting in a decrease of the atomic number by two and the mass number by four. Beta decay, on the other hand, involves the conversion of a neutron into a proton with the emission of a beta particle (electron), increasing the atomic number by one. Recognizing these processes is vital for constructing the decay series accurately.

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