To determine which of the given reactions represents beta decay, we need to review the basic process of beta decay. Beta decay involves the conversion of a neutron into a proton within an atomic nucleus, with the emission of a beta particle (an electron) and an antineutrino. Let's examine each option:
Option A: [tex]\( {}_{64}^{160} Gd \rightarrow_{65}^{160} Tb+{}^{0} e \)[/tex]
- In this reaction, a gadolinium (Gd) nucleus is transforming into a terbium (Tb) nucleus.
- The atomic number of gadolinium (Gd) increases from 64 to 65, indicating the conversion of a neutron into a proton and the emission of a beta particle.
- This matches the definition of beta decay.
Option B: [tex]\( {}_{64}^{148} Gd \rightarrow {}_{62}^{144} Sm + {}_{2}^{4} He \)[/tex]
- Here, a gadolinium (Gd) nucleus is transforming into a samarium (Sm) nucleus along with the emission of an alpha particle (helium nucleus).
- The transformation involves a decrease in the atomic number from 64 to 62.
- This is not beta decay; it is alpha decay.
Option C: [tex]\( {}_{43}^{98} Tc \rightarrow {}_{43}^{98} Tc + \gamma \)[/tex]
- In this reaction, a technetium (Tc) nucleus remains unchanged and emits a gamma ray ([tex]\(\gamma\)[/tex]).
- The atomic number and mass number remain the same.
- This is gamma decay, not beta decay.
Option D: [tex]\( {}_{63}^{150} Eu + {}_{-1}^{0} e \rightarrow {}_{62}^{150} Sm \)[/tex]
- Here, a europium (Eu) nucleus captures an electron, leading to a decrease in the atomic number from 63 to 62.
- Electron capture is different from beta decay.
Given the breakdown of each option, the reaction that correctly represents beta decay is:
Option A: [tex]\( {}_{64}^{160} Gd \rightarrow_{65}^{160} Tb+{}^{0} e \)[/tex]
Thus, the correct choice is 1.
