Alpha decay bookkeeping: when the isotope 92U238 emits one alpha (α) particle, what is the resulting daughter nuclide (give the correct element and mass/atomic numbers)?

Introduction / Context:
Alpha decay subtracts a helium nucleus (two protons and two neutrons) from a parent nuclide. Correctly writing alpha-decay products is a foundational skill in nuclear chemistry and reactor physics because it enforces conservation of nucleon number and charge while identifying the right element symbol from the periodic table.

Given Data / Assumptions:

• Parent: 92U238 (uranium-238).
• One alpha particle emitted: 2 protons + 2 neutrons, symbolically 2He4.
• Mass number and atomic number must be conserved.

Concept / Approach:
Conservation relations for alpha decay are straightforward: A_daughter = A_parent − 4, Z_daughter = Z_parent − 2. Subtracting 2 from Z changes the chemical element to the one two places earlier in the periodic table. For uranium (Z = 92), the daughter has Z = 90, which corresponds to thorium (Th). The mass number decreases from 238 to 234.

Step-by-Step Solution:
Write A_parent = 238, Z_parent = 92.Apply alpha emission: A_daughter = 238 − 4 = 234; Z_daughter = 92 − 2 = 90.Map Z_daughter = 90 to element symbol: Th (thorium).State daughter nuclide: 90Th234.

Verification / Alternative check:
Check conservation explicitly: Left side nucleons 238, right side 234 + 4 = 238; charges 92, right side 90 + 2 = 92. Both balances hold, confirming the result.

Why Other Options Are Wrong:
90U234: Wrong element; Z = 90 is thorium, not uranium.90Pa234: Protactinium is Z = 91, not 90; also alpha decay from U-238 goes to Th-234.92U236: Would require neutron emission, not alpha; alpha decay lowers Z by 2.88Ra234: Z = 88 would require emitting more than an alpha or a different decay chain.

Common Pitfalls:
Keeping the element symbol as U after changing Z, or mixing up Pa (Z = 91) and Th (Z = 90). Always translate atomic number to the correct periodic symbol after the arithmetic.

Final Answer:
90Th234