To determine which daughter element is produced from the beta decay of [tex]\({ }_{36}^{89} Kr\)[/tex], we need to understand the process of beta decay.
In beta decay:
1. A neutron in the nucleus transforms into a proton.
2. This transformation results in the release of an electron (beta particle).
3. As a neutron becomes a proton, the atomic number (Z) increases by 1, while the atomic mass number (A) remains unchanged.
Given the initial element:
- Atomic number (Z) of Krypton ([tex]\(Kr\)[/tex]): 36
- Atomic mass number (A) of Krypton: 89
After beta decay:
- The atomic number (Z) will increase by 1: [tex]\( 36 + 1 = 37 \)[/tex]
- The atomic mass number (A) remains the same: 89
The new element with an atomic number [tex]\(Z = 37\)[/tex] and an atomic mass [tex]\(A = 89\)[/tex] corresponds to Rubidium (Rb). Hence, the daughter element produced from the beta decay of [tex]\({ }_{36}^{89} Kr\)[/tex] is Rubidium, [tex]\({ }_{37}^{89} Rb\)[/tex].
Therefore, the correct answer is:
D. [tex]\({ }_{37}^{89} Rb\)[/tex]
