Question

In the nuclear reaction \( \mathrm{^{10}_{5}B} + \mathrm{^{4}_{2}He} \rightarrow X + \mathrm{^{1}_{0}n} \), X represents:

• A. \( \mathrm{^{12_{6C }}}\)
• B. \( \mathrm{^{13_{7N}}} \)
• C. \( \mathrm{^{14_{7N}}} \)
• D. \( \mathrm{^{13_{6C}}} \)

Hint:

Key Points: Conservation laws in nuclear reactions: Total mass number (A) must balance Total atomic number (Z) must balance \( \mathrm{^{4_{2He \) is an alpha particle \( \mathrm{^{1_{0n \) is a neutron This is an example of an alpha particle-induced nuclear reaction

Answer 1

The Correct Option is B

To determine the unknown nucleus X, we balance both mass numbers (superscripts) and atomic numbers (subscripts):

• Mass number balance: \( 10 \text{ (B)} + 4 \text{ (He)} = A\text{(X)} + 1 \text{ (n)} \) \( 14 = A + 1 \Rightarrow A = 13 \)
• Atomic number balance: \( 5 \text{ (B)} + 2 \text{ (He)} = Z\text{(X)} + 0 \text{ (n)} \) \( 7 = Z \)

Thus, X must be \( \mathrm{^{13}_{7}N} \) (Nitrogen-13).

Verification of other options:

• (A) \( \mathrm{^{12}_{6}C} \): Incorrect mass number and atomic number
• (C) \( \mathrm{^{14}_{7}N} \): Incorrect mass number
• (D) \( \mathrm{^{13}_{6}C} \): Incorrect atomic number