To determine which element completes the given beta decay reaction, let's analyze what happens during a beta decay process.
Beta Decay Process:
- In beta decay, a neutron in the nucleus is transformed into a proton and an electron (beta particle, denoted as [tex]\(\beta^{-}\)[/tex]) is emitted.
- The atomic number of the element increases by 1 because we gain a proton.
- The mass number (the total number of protons and neutrons) does not change because the total number of nucleons remains the same.
Given:
- The initial element is sulfur ([tex]\(S\)[/tex]) with an atomic number of 16 and a mass number of 33.
- We represent sulfur as [tex]\({ }_{16}^{33} S\)[/tex].
- A beta particle [tex]\(\beta^{-}\)[/tex] (with atomic number -1 and mass number 0) is emitted.
The reaction can be written as:
[tex]\[ { }_{16}^{33} S \rightarrow \square + { }_{-1}^0 \beta \][/tex]
1. Determine the new atomic number:
- Initial atomic number of sulfur ([tex]\(S\)[/tex]) = 16
- After beta decay, the new atomic number ([tex]\(Z'\)[/tex]) is:
[tex]\[
Z' = 16 + 1 = 17
\][/tex]
2. Determine the new mass number:
- Initial mass number remains unchanged because the total number of nucleons does not change.
[tex]\[
A' = 33
\][/tex]
3. Identify the new element:
- An atomic number of 17 corresponds to the element Chlorine ([tex]\(Cl\)[/tex]).
Therefore, completing the beta decay reaction, the new element is chlorine with atomic number 17 and mass number 33, represented as [tex]\(\boxed{{ }_{17}^{33} Cl}\)[/tex].
So, the missing item in the reaction:
[tex]\[
\boxed{{ }_{17}^{33} Cl}
\][/tex]
Thus, the correct answer is:
C. \quad{ }_{17}^{33} Cl
