Final answer:
To describe a decay chain such as thorium-228 to lead-208, a series of nuclear decay equations show the emission of alpha and beta particles, leading to the formation of the stable nucleus, lead-208, while adhering to conservation laws.
Step-by-step explanation:
Writing a series of nuclear decay equations is essential for illustrating the sequence of transformations that an unstable nucleus undergoes to reach a stable state. As an example to describe the decay chain from thorium-228 to lead-208, we consider a series of alpha (\( \alpha \)) and beta (\( \beta \)) particle emissions. Decay reactions can be represented by nuclear equations which show the initial nucleus, the particles being emitted, and the resulting nucleus.
- Thorium-228 (\(^{228}_{90}Th\)) undergoes an alpha decay to emit an alpha particle (\(^{4}_{2}He\)) and forms radium-224 (\(^{224}_{88}Ra\)).
- Radium-224 further decays by emitting an alpha particle to form radon-220 (\(^{220}_{86}Rn\)).
- This process continues with a series of alpha and beta decays until lead-208 (\(^{208}_{82}Pb\)) is formed, which is a stable nucleus.
Each alpha decay decreases the atomic number by 2 and the mass number by 4, while beta decay increases the atomic number by 1 without changing the mass number. Ensuring that conservation laws for charge, baryon number, lepton number, and energy are satisfied is crucial when writing these equations.