To determine the missing item that completes the given beta decay reaction, we need to understand the process of beta decay and how it affects the atomic and mass numbers of an element.
The given reaction is:
[tex]\[
{}_{43}^{98} \text{Tc} \rightarrow {}_{44}^{98} \text{Ru} + \, ?
\][/tex]
### Step-by-Step Explanation:
1. Understand Beta Decay:
- In beta-minus (β−) decay, a neutron in the nucleus is converted into a proton, and in the process, an electron (beta particle, β−) and an antineutrino are emitted.
- The proton number (atomic number) increases by 1.
- The mass number remains unchanged.
2. Observing the Change in the Given Reaction:
- The atomic number of Technetium (Tc) is 43.
- The atomic number of Ruthenium (Ru) is 44.
- Since the atomic number increases from 43 (Tc) to 44 (Ru), it suggests a neutron has been converted into a proton.
- The mass number stays the same (98 remains 98).
3. Identifying the Missing Particle:
- According to the above points, the missing particle must be an electron (beta particle, β−), which is emitted during beta-minus decay.
- The symbol for an electron (beta particle) in beta-minus decay is [tex]\( {}_{-1}^0 \beta \)[/tex].
4. Verifying With Options:
- A. [tex]\( {}_{-1}^0 \beta \)[/tex]
- B. [tex]\( {}_0^0 \gamma \)[/tex]: This represents a gamma photon, which does not change atomic or mass numbers.
- C. [tex]\( {}_2^4 \text{He} \)[/tex]: This represents an alpha particle, which would decrease the mass number by 4 and the atomic number by 2.
- D. [tex]\( {}_1^0 n \)[/tex]: This represents a neutron, which is not relevant to this type of decay.
Since only option A correctly represents the particle emitted in beta-minus decay, the correct choice is:
[tex]\[
\boxed{{}_{-1}^0 \beta}
\][/tex]
