Question

The isotope ²³⁴92U undergoes five successive alpha decays. Identify the correct decay chain.

a ²³³₉₀Th --> ²²⁹₈₈Ra --> ²²⁵₈6Rn --> ²¹⁸₈₄Po --> ²¹⁷₈₂Pb
b. ²²⁸₉₀Th --> ²²⁸₈₈Ra --> ²²⁸₈6Rn --> ²¹⁸₈₄Po --> ²¹²₈₂Pb
c. ²³²₉₀Th --> ²²⁸₈₈Ra --> ²²⁸₈6Rn --> ²²⁰₈₄Po --> ²¹⁶₈₂Pb
d. ²³⁰₉₀Th --> ²²⁶₈₈Ra --> ²²²₈6Rn --> ²¹⁸₈₄Po --> ²¹⁴₈₂Pb

Answer 1

The isotope U-234 undergoes five successive alpha decays leading to the formation of Pb-214. However, none of the provided options match the correct decay sequence, suggesting an error in the question. The correct sequence reduces the atomic number by 2 and the mass number by 4 for each alpha decay.

Step-by-step explanation:

The isotope U-234 undergoes five successive alpha decays. To identify the correct decay chain, we must account for a decrease of 2 in atomic number (Z) and 4 in mass number with each alpha decay. Starting with U-234 (Z=92), the successive decays with the corresponding atomic numbers are:

• Th-230 (Z=90)
• Ra-226 (Z=88)
• Rn-222 (Z=86)
• Po-218 (Z=84)
• Pb-214 (Z=82)

Therefore, matching these decays with the options given, the correct decay chain is:

²³⁴₉₂U --> ²³⁰₉₀Th --> ²²⁶₈₈Ra --> ²²²₈₆Rn --> ²¹⁸₈₄Po --> ²¹⁴₈₂Pb

This decay chain does not match any of the options provided, which indicates a potential error in the question. According to standard alpha decay sequences, the given isotope U-234 undergoes the chain specified above, resulting in lead-214 (Pb-214).