Chapter 30, Problem 24Q

To determine

The number of alpha and beta particles emitted when Radon decays into lead.

The importance of path in the decay series is chosen.

Answer to Problem 24Q

Solution:

Four alpha particles and four beta particles emitted when Radon decays into lead,no matter which decay path is chosen.

Explanation of Solution

When $Rn$ decays into $Pb$ , it will emit a certain number of alpha and beta particles.The nucleon number drops by 16 as 222 of Rn decreases to 206 of lead.

Atomic number 86 which is Rn, decays into atomic number 82 which is Pb, indicating that four alpha decays occurred. The proton number drops only by four, from atomic number 86 to 82 but four alpha decays would result in a decrease of eight protons. Four beta decays will convert the remaining four neutrons into protons so that protons decrease to only four.

Conclusion:

Four alpha particles and four beta particles are emitted when Radon decays into lead, no matter which decay path is chosen.