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

Verified step by step guidance

1. insert step 1> Identify the initial isotope: Thorium-232 (\(^{232}_{90}\text{Th}\)).
2. 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 \(^{228}_{88}\text{Ra}\).
3. 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 \(^{228}_{89}\text{Ac}\).
4. insert step 4> Apply the third decay: Another beta decay increases the atomic number by 1 again, resulting in \(^{228}_{90}\text{Th}\).
5. insert step 5> Apply the fourth decay: Another alpha decay reduces the atomic number by 2 and the mass number by 4, resulting in \(^{224}_{88}\text{Ra}\).

Key Concepts

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.