Question

The number of alpha (\(\alpha\)) particles emitted to produce a daughter isotope of \(^{206}\text{Pb}\) from a parent isotope of \(^{238}\text{U}\) by radioactive decay is ........

Hint:

In radioactive decay chains, the number of alpha particles emitted can be determined by counting the steps of alpha decay until a stable isotope is formed.

Answer 1

Correct Answer: 8

Step 1: Understanding the decay process.
The radioactive decay of uranium-238 (\(^{238}\text{U}\)) follows a chain of alpha and beta decays until it forms stable lead-206 (\(^{206}\text{Pb}\)). To calculate the number of alpha particles emitted, we look at the decay chain.

Step 2: Analyzing the decay chain.
The decay of \(^{238}\text{U}\) to \(^{206}\text{Pb}\) involves the emission of 8 alpha particles. This is because \(^{238}\text{U}\) decays to \(^{234}\text{Th}\), and through subsequent decays, eventually leads to \(^{206}\text{Pb}\), with 8 total alpha emissions.

Step 3: Conclusion.
The number of alpha particles emitted is 8.