Certainly! Let’s analyze the given nuclear reaction step-by-step:
### Given Reaction:
[tex]\[ {}_2^4 \text{He} \rightarrow ? + {}_{-1}^0 e \][/tex]
Step 1: Understanding the Particles Involved
- Helium nucleus (Alpha particle):
- Mass number (A): 4
- Atomic number (Z): 2
- Beta particle (Electron):
- Mass number (A): 0
- Atomic number (Z): -1
### Step 2: Conservation of Mass Number and Atomic Number
For a nuclear reaction, both the mass number and atomic number must be conserved. This means the sum of the mass numbers and the sum of the atomic numbers on both sides of the equation must be equal.
- Mass Number Conservation:
[tex]\[ 4 = A + 0 \][/tex]
- This implies the mass number (A) of the unknown particle should be 4.
- Atomic Number Conservation:
[tex]\[ 2 = Z + (-1) \][/tex]
- This implies the atomic number (Z) of the unknown particle should be 3.
### Step 3: Identifying the Unknown Particle
Now that we have found the mass number and atomic number of the unknown particle:
- Mass number (A): 4
- Atomic number (Z): 3
The element with atomic number 3 is Lithium (Li).
### Conclusion
The nuclear reaction completes as follows:
[tex]\[ {}_2^4 \text{He} \rightarrow {}_3^4 \text{Li} + {}_{-1}^0 e \][/tex]
So, the unknown particle is a lithium-4 nucleus:
[tex]\[ {}_3^4 \text{Li} \][/tex]
