Question

Consider the following radioactive decay process

Hint:

$\alpha$-decay reduces atomic number by 2 and mass number by 4, while $\beta^-$-decay increases atomic number by 1

Answer 1

Correct Answer: 4

Step 1: Balance mass number.
Seven alpha particles carry away the mass, so $238 = 210 + 7\times 4$, and no extra alpha is needed.

Step 2: Balance atomic number.
Seven alphas lower the atomic number by 14, from 92 to 78, but the product needs 82.

Step 3: Add beta decays.
Each beta minus raises the number by one, so we need $82 - 78 = 4$ beta decays.

Step 4: Answer.
\[ \boxed{4} \]