To solve this problem, we need to ensure that the nuclear equation is balanced both in terms of the mass number (A) and the atomic number (Z). Let's consider the given nuclear equation:
[tex]\[ _{11}^{22} \text{Na} \longrightarrow _{10}^{22} \text{Ne} + _{2}^0 \text{B} \][/tex]
1. Identify the mass numbers and atomic numbers of the involved particles:
- Sodium-22 (Na) has a mass number [tex]\(22\)[/tex] and an atomic number [tex]\(11\)[/tex]: [tex]\[ _{11}^{22} \text{Na} \][/tex]
- Neon-22 (Ne) has a mass number [tex]\(22\)[/tex] and an atomic number [tex]\(10\)[/tex]: [tex]\[ _{10}^{22} \text{Ne} \][/tex]
- The particle we are looking to identify is denoted as: [tex]\[ _{2}^0 \text{B} \][/tex]
2. Balance the mass numbers:
- The mass number on the left side of the equation (Sodium-22, Na) is [tex]\(22\)[/tex].
- The mass number on the right side of the equation (Neon-22, Ne) is also [tex]\(22\)[/tex].
- Since the mass numbers are already balanced, the missing particle should have a mass number of [tex]\(0\)[/tex].
3. Balance the atomic numbers:
- The atomic number on the left side of the equation (Sodium-22, Na) is [tex]\(11\)[/tex].
- The atomic number on the right side is the sum of the atomic numbers of Neon (Ne), which is [tex]\(10\)[/tex], and the unknown particle (B).
To balance the atomic numbers, we need:
[tex]\[ \text{atomic number of Na} = \text{atomic number of Ne} + \text{atomic number of B} \][/tex]
[tex]\[ 11 = 10 + \text{atomic number of B} \][/tex]
Hence, the atomic number of the unknown particle (B) must be:
[tex]\[ \text{atomic number of B} = 11 - 10 = 1 \][/tex]
So, the missing particle has a mass number of [tex]\(0\)[/tex] and an atomic number of [tex]\(1\)[/tex].
Among the given answer choices:
- [tex]\(-1\)[/tex]
- [tex]\(0\)[/tex]
- [tex]\(+1\)[/tex]
- [tex]\(+2\)[/tex]
The correct value that will balance the equation is [tex]\(+1\)[/tex].
