A radioactive decay series that begins with 232₉₀Th ends with the formation of the stable nuclide 208₈₂Pb. How many alpha-particle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?

Verified step by step guidance

1. Step 1: Understand the problem by identifying the initial and final nuclides in the decay series. The series starts with Thorium-232 (\(^{232}_{90}\text{Th}\)) and ends with Lead-208 (\(^{208}_{82}\text{Pb}\)).
2. Step 2: Determine the change in atomic number and mass number. The atomic number changes from 90 to 82, and the mass number changes from 232 to 208.
3. Step 3: Calculate the total change in mass number. Subtract the final mass number from the initial mass number: 232 - 208 = 24. Each alpha particle emission reduces the mass number by 4, so divide the total change in mass number by 4 to find the number of alpha emissions.
4. Step 4: Calculate the total change in atomic number. Subtract the final atomic number from the initial atomic number: 90 - 82 = 8. Each alpha particle emission reduces the atomic number by 2, so multiply the number of alpha emissions by 2 and subtract from the total change in atomic number to find the number of beta emissions.
5. Step 5: Verify the solution by ensuring that the calculated number of alpha and beta emissions account for the changes in both atomic and mass numbers, confirming the decay series transformation from \(^{232}_{90}\text{Th}\) to \(^{208}_{82}\text{Pb}\).

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 and beta decay. In alpha decay, an atomic nucleus emits an alpha particle (two protons and two neutrons), while in beta decay, a neutron is transformed into a proton, emitting a beta particle (an electron or positron). Understanding these processes is crucial for analyzing decay series.

Alpha and Beta Particles

Alpha particles are positively charged particles consisting of two protons and two neutrons, effectively reducing the atomic number of the parent nuclide by two and the mass number by four. Beta particles, on the other hand, are high-energy, high-speed electrons or positrons emitted from a decaying nucleus, which increases the atomic number by one without changing the mass number. The type and number of emissions determine the transformation of the original nuclide into a stable product.

Decay Series

A decay series is a sequence of radioactive decays that a particular nuclide undergoes until it reaches a stable end product. Each step in the series involves either alpha or beta decay, leading to different intermediate nuclides. In the case of 232Th decaying to 208Pb, tracking the number of alpha and beta emissions is essential to understand the complete transformation and the final stable nuclide formed.