Let's analyze the given nuclear reaction and determine which nucleus completes it.
The problem presented is:
[tex]\[ _{17}^{39} Cl \rightarrow \,_{-1}^{0} e + \, ? \][/tex]
We are dealing with the isotope of chlorine, [tex]\[ _{17}^{39} Cl \][/tex], which has:
- Atomic number (Z) = 17 (protons)
- Mass number (A) = 39 (protons + neutrons)
1. Identify the Decay Process:
The chlorine isotope [tex]\[ _{17}^{39} Cl \][/tex] undergoes beta decay, which is indicated by the emission of a beta particle [tex]\[ _{-1}^{0} e \][/tex]. In beta decay, a neutron in the nucleus converts into a proton and emits a beta particle (electron).
2. Effect of Beta Decay:
- A neutron changes into a proton.
- The atomic number (Z) increases by 1, because the number of protons increases by 1.
- The mass number (A) remains the same because the total number of nucleons (protons + neutrons) does not change.
3. Calculate the New Atomic Number:
Since the original chlorine nucleus has 17 protons, after gaining one proton from the decay of a neutron, the new atomic number will be:
[tex]\[
17 + 1 = 18
\][/tex]
4. Determine the New Element:
An atomic number of 18 corresponds to the element Argon (Ar).
5. Mass Number:
The mass number remains unchanged at 39 because the total number of nucleons is the same.
6. Final Nucleus:
The resulting nucleus is:
[tex]\[ _{18}^{39} Ar \][/tex]
Thus, the nucleus that completes the equation [tex]\[ _{17}^{39} Cl \rightarrow \,_{-1}^{0} e + \, ? \][/tex] is [tex]\[ _{18}^{39} Ar \][/tex], which corresponds to option:
b. [tex]\[ _{18}^{39} Ar \][/tex]
So, the correct answer is:
[tex]\[ \boxed{b} \][/tex]
