Write balanced nuclear equations for the following transformations:
(b) nitrogen-13 undergoes electron capture.

Verified step by step guidance

1. Identify the process: Electron capture involves an inner orbital electron being captured by the nucleus, which combines with a proton to form a neutron.
2. Write the initial isotope: Nitrogen-13 is represented as \( ^{13}_{7}\text{N} \).
3. Apply the electron capture process: An electron (\( ^{0}_{-1}\text{e} \)) is captured by the nucleus.
4. Determine the resulting isotope: The capture of an electron by a proton in the nucleus converts the proton into a neutron, resulting in Carbon-13, \( ^{13}_{6}\text{C} \).
5. Write the balanced nuclear equation: \( ^{13}_{7}\text{N} + ^{0}_{-1}\text{e} \rightarrow ^{13}_{6}\text{C} \).

Key Concepts

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus, resulting in the transformation of one element into another. These reactions can include processes such as alpha decay, beta decay, and electron capture, where particles are emitted or absorbed, altering the atomic number and mass number of the original atom.

Electron Capture

Electron capture is a type of radioactive decay in which an electron from the innermost energy level is captured by the nucleus, combining with a proton to form a neutron. This process decreases the atomic number of the element by one, effectively transforming it into a different element while the mass number remains unchanged.

Balancing Nuclear Equations

Balancing nuclear equations requires ensuring that the total number of protons and neutrons is the same on both sides of the equation. This involves accounting for the changes in atomic and mass numbers resulting from the nuclear transformation, ensuring that the equation adheres to the conservation of mass and charge principles.