Let's start by understanding what happens when a nuclide of [tex]\({ }_{29}^{64} Cu\)[/tex] (Copper-64) absorbs a positron.
1. Positron Absorption:
- A positron (essentially the antiparticle of an electron with a positive charge) interacts with a nucleus.
- This interaction converts a proton into a neutron.
2. Impact on the Atomic Number and Mass Number:
- When a proton is converted into a neutron:
- The atomic number decreases by 1 because there is one less proton.
- The mass number remains unchanged because the overall number of nucleons (protons and neutrons) stays the same.
Given:
- The initial atomic number of the atom is 29 (Copper - Cu).
- The initial mass number is 64.
After the positron absorption:
- The atomic number decreases by 1:
[tex]\[
29 - 1 = 28
\][/tex]
- The mass number remains the same:
[tex]\[
64
\][/tex]
An element with an atomic number of 28 is Nickel (Ni).
Therefore, the resulting atom after the absorption of a positron by [tex]\({ }_{29}^{64} Cu\)[/tex] is [tex]\({ }_{28}^{64} Ni\)[/tex].
Among the given options:
[tex]\[
\boxed{{ }_{28}^{64} Ni}
\][/tex]
