To determine the product of the beta decay of Thallium-206 ([tex]\(^{206}_{81} \text{Tl}\)[/tex]), let's first review what happens during beta decay.
1. Understanding Beta Decay:
- In beta decay, a neutron in the nucleus is converted into a proton.
- This process emits an electron (known as a beta particle) and an anti-neutrino.
- As a result, the atomic number (number of protons) of the element increases by 1.
- Importantly, the mass number (sum of protons and neutrons) remains unchanged.
2. Initial Element Information:
- The initial element is Thallium-206 ([tex]\(^{206}_{81} \text{Tl}\)[/tex]).
- The atomic number is 81, which means Thallium has 81 protons.
- The mass number is 206, indicating the total number of protons and neutrons.
3. Change in Atomic Number:
- During beta decay, the atomic number increases by 1.
- Therefore, the atomic number after decay will be [tex]\(81 + 1 = 82\)[/tex].
4. Mass Number Remains Constant:
- The mass number will remain the same at 206.
5. Identifying the Final Element:
- The new element has an atomic number of 82 and a mass number of 206.
- The element with atomic number 82 is Lead (Pb).
Based on the information above, the other product of the beta decay of [tex]\(^{206}_{81} \text{Tl}\)[/tex] is:
[tex]\[
^{206}_{82} \text{Pb}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{^{206}_{82} \text{Pb}}
\][/tex]
