Radon-222 decays by a series of three a emissions and two b emissions. What is the final stable nucleus?

Verified step by step guidance

1. Identify the initial nucleus: Radon-222 (\(^{222}_{86}\text{Rn}\)).
2. Understand that an alpha (\(\alpha\)) emission decreases the atomic number by 2 and the mass number by 4. Therefore, after three \(\alpha\) emissions, the atomic number decreases by 6 and the mass number decreases by 12.
3. Recognize that a beta (\(\beta\)) emission increases the atomic number by 1 while the mass number remains unchanged. Therefore, after two \(\beta\) emissions, the atomic number increases by 2.
4. Calculate the new atomic number: Start with 86 (Radon), subtract 6 (from three \(\alpha\) emissions), and add 2 (from two \(\beta\) emissions).
5. Calculate the new mass number: Start with 222, subtract 12 (from three \(\alpha\) emissions), and note that \(\beta\) emissions do not change the mass number.

Key Concepts

Alpha Decay

Alpha decay is a type of radioactive decay in which an unstable nucleus emits an alpha particle, consisting of two protons and two neutrons. This process decreases the atomic number by two and the mass number by four, resulting in a new element. Understanding alpha decay is crucial for tracking the changes in the nucleus as it transforms into a more stable form.

Beta Decay

Beta decay occurs when a neutron in an unstable nucleus is transformed into a proton, emitting a beta particle (an electron or positron) in the process. This increases the atomic number by one while keeping the mass number unchanged. Recognizing how beta decay alters the composition of the nucleus is essential for determining the final stable nucleus after a series of emissions.

Nuclear Stability

Nuclear stability refers to the ability of a nucleus to remain intact without undergoing radioactive decay. Stable nuclei have a balanced ratio of protons to neutrons, which minimizes repulsive forces between protons. Identifying the final stable nucleus after a series of decay events requires understanding the stability criteria for different isotopes and how they evolve through decay processes.