To determine which particle correctly completes the radioactive decay equation for Carbon-11, we need to ensure that both the mass number (nucleon number) and the atomic number (proton number) are balanced on both sides of the equation.
The given equation is:
[tex]\[
{}_{6}^{11} \text{C} \rightarrow {}_{5}^{11} \text{B} + \text{?}
\][/tex]
### Step-by-Step Solution:
1. Mass Number (Nucleon Number) Balance:
- On the left side (Carbon-11): Mass number is 11.
- On the right side (Boron-11 + ?:):
- Boron-11 has a mass number of 11.
- The unknown particle must have a mass number such that the total mass number on the right also equals 11.
- Since Boron-11 already has a mass number of 11, the unknown particle must have a mass number of 0 to keep the total mass number on the right as 11.
2. Atomic Number (Proton Number) Balance:
- On the left side (Carbon-11): Atomic number is 6.
- On the right side (Boron-11 + ?):
- Boron-11 has an atomic number of 5.
- The unknown particle must have an atomic number such that the total atomic number on the right also equals 6.
- The atomic number of 5 (Boron-11) plus the atomic number of the unknown particle must equal 6.
- Therefore, the unknown particle must have an atomic number of 1 (since 5 + 1 = 6).
Given these requirements, let's check the provided options:
A. [tex]\({ }_{-1}^0 e\)[/tex]
- Mass number: 0 (correct)
- Atomic number: -1 (not correct, we need +1)
B. [tex]\({}_{+1}^0 e\)[/tex]
- Mass number: 0 (correct)
- Atomic number: +1 (correct)
C. [tex]\({}_{4}^{2} \text{He}\)[/tex]
- Mass number: 4 (not correct, we need 0)
- Atomic number: 2 (not correct, we need +1)
D. [tex]\({}_{2}^{4} \text{He}\)[/tex]
- Mass number: 4 (not correct, we need 0)
- Atomic number: 2 (not correct, we need +1)
From the options given, Option B ([tex]\({ }_{+1}^0 e\)[/tex]) is the only particle that correctly balances both the mass number and the atomic number in the decay equation.
Thus, the correct answer is:
[tex]\[
\boxed{{ }_{+1}^0 e}
\][/tex]
