Question

Which of the following correctly identifies the following process? $$_{31}^{67} \mathrm{Ga}+e^{-} \rightarrow_{30}^{67} \mathrm{Zn}$$ A. \(\beta^{-}\) decay B. \(\beta^{+}\) decay C. \(e^{-}\) capture D. \(\gamma\) decay

Short answer

C. Electron capture

Step-by-step solution

- Analyze the Given Reaction

Examine the initial and final elements in the reaction. The reaction given is \( _{31}^{67} \mathrm{Ga} + e^{-} \rightarrow _{30}^{67} \mathrm{Zn} \). Compare the atomic numbers and mass numbers of Gallium (Ga) and Zinc (Zn).

- Identify the Changes in Atomic Number

Notice that the atomic number decreases from 31 to 30, while the mass number remains at 67. This suggests that a proton has been converted into a neutron.

- Consider the Role of the Electron

Observe that an electron (\( e^{-} \)) is being added to the nucleus. This electron interacts with a proton, converting it to a neutron.

- Identify the Nuclear Process

The process where an electron is captured by the nucleus and a proton is converted into a neutron is known as electron capture (\( e^{-} \) capture).

- Compare with Multiple Choices

A. \( \beta^{-} \) decay involves a neutron converting into a proton, which is not the case here. B. \( \beta^{+} \) decay involves a proton converting into a neutron and emitting a positron, not an electron capture. C. Electron capture (\( e^{-} \) capture) matches our analysis. D. \( \gamma \) decay involves energy emission without changing atomic or mass numbers.

Key concepts

Electron Capture

Electron capture is a process in which an atomic nucleus absorbs an inner orbital electron. This process decreases the number of protons in the nucleus and increases the number of neutrons. As a result, the atomic number of the element decreases by one, while the mass number remains unchanged. This reaction is commonly represented as:
$$ \text{_Z^A X} + e^{-} \rightarrow \text{_{Z-1}^A Y} $$
where \text{_Z^A X} is the initial element, and \text{_{Z-1}^A Y} is the element after electron capture. For example, in the reaction \text{{\(_{31}^{67} \text{Ga} + e^{-} \rightarrow_{30}^{67} \text{Zn}\)}}, the electron combines with a proton in the Gallium nucleus (Ga), converting it into a neutron and thereby transforming Gallium (atomic number 31) into Zinc (atomic number 30).

Atomic Number Changes

In nuclear reactions, the atomic number changes can often indicate the type of process involved. For example, in electron capture, the atomic number decreases by one.
This is because a proton in the nucleus captures an electron and transforms into a neutron:
\text{{\(_{Z}^{A}X\)}} + \({e^{-}}\) \rightarrow \text{{\(_{Z-1}^{A}Y\)}}.
Here, Z decreases by one, but the mass number A remains constant.
Understanding how atomic numbers change in various nuclear reactions is crucial in identifying the reaction type. For instance, \text{{\(_{31}^{67} \text{Ga}\)}} becomes \text{{\(_{30}^{67} \text{Zn}\)}} after capturing an electron.

Neutron-Proton Conversion

Neutron-proton conversion plays a significant role in nuclear decay processes. In the context of electron capture, a proton in the nucleus captures an electron and converts into a neutron.
The reaction for neutron-proton conversion via electron capture can be written as:
\text{{\(_{Z}^{A}X\)}} + \(e^{-}\) \rightarrow \text{{\(_{Z-1}^{A}Y\)}}.
During the process, the atomic number (Z) of the nucleus decreases by one, as a proton (p) turns into a neutron (n). This does not change the mass number (A).
Understanding this conversion helps explain changes in atomic structure during different types of nuclear reactions.

Nuclear Decay Processes

Nuclear decay processes include several types, such as \text{\(\beta^{-}\)} decay, \text{\(\beta^{+}\)} decay, \text{electron capture}, and \text{\(\text{\)\text{\(-\text {\)-\text {\(\beta^{-}\) decay involves a neutron converting into a proton}, typically emitting an electron {(e^{-})} and an antineutrino {(ν̅)}.
\(\beta^{+} decay involves a proton converting into a neutron, emitting a positron {(e^{+})} and a neutrino {(ν)}.
Electron capture {(e^{-}) occurs when a proton in the nucleus captures an electron}, converting it into a neutron}.
Finally, gamma (\text{\){gamma decay}\() involves the emission of energy} \br> \)\backslash` typically as a gamma ray, without altering the atomic or mass nucleas. \br> Understanding different nuclear decay processes helps in identifying the correct type of reaction based on changes in atomic numbers and emitted particles, as seen in the example \text{\(_{31}^{67}Ga} +\)} \(\text{{e^{-}}}\) $\rightarrow {_ {30}^{67} Zn}.\text{