Bismuth-212 attaches readily to monoclonal antibodies and is used in the treatment of various cancers. This bismuth-212 is formed after the parent isotope undergoes a decay series consisting of four α decays and one β decay (the decays could be in any order). What is the parent isotope for this decay series?

Verified step by step guidance

1. Identify the changes in atomic number and mass number for each type of decay: $\alpha$ decay decreases the atomic number by 2 and the mass number by 4, while $\beta$ decay increases the atomic number by 1 and does not change the mass number.
2. Calculate the total change in atomic number after four $\alpha$ decays and one $\beta$ decay: $4\times (-2)+1\times (+1)=-7$.
3. Calculate the total change in mass number after four $\alpha$ decays: $4\times (-4)=-16$.
4. Determine the atomic number and mass number of the parent isotope by adding the changes to the atomic number and mass number of Bismuth-212: Atomic number of parent = 83 (Bismuth) + 7, Mass number of parent = 212 + 16.
5. Identify the element with the calculated atomic number to find the parent isotope.

Key Concepts

Decay Series

A decay series refers to a sequence of radioactive decays that a parent isotope undergoes to transform into a stable or different isotope. In this context, the parent isotope decays through a series of alpha (α) and beta (β) decays, resulting in the formation of bismuth-212. Understanding the types of decay and their order is crucial for identifying the parent isotope.

Alpha and Beta Decay

Alpha decay involves the emission of an alpha particle (two protons and two neutrons), resulting in a decrease in 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 (an electron), increasing the atomic number by one. Recognizing how these decays affect the isotopes is essential for tracing the decay path back to the parent isotope.

Isotope Identification

Isotope identification involves determining the specific isotope of an element based on its atomic number and mass number. In the case of bismuth-212, it is important to trace back through the decay series to find the original isotope that leads to its formation. This requires knowledge of the isotopes involved in the decay process and their respective properties.