Question

Fill in the following table: $$ \begin{array}{lcc} \text { Event } & \begin{array}{c} \text { Change in } \\ \text { Atomic Number } \end{array} & \begin{array}{c} \text { Change in } \\ \text { Mass Number } \end{array} \\ \hline \alpha \text { -decay } & & \\ \beta \text { -emission } & & \\ \text { positron emission } & & \\ \text { K-electron capture } & & \\ \gamma \text {-decay } & & & \end{array} $$

Short answer

Answer: During K-electron capture, the atomic number decreases by 1 and the mass number remains unchanged.

Step-by-step solution

Complete Information About Each Nuclear Reaction

We'll start by providing a brief overview of each nuclear reaction and how it affects the atomic number and mass number: 1. Alpha decay: In this process, the nucleus emits an alpha particle composed of 2 protons and 2 neutrons. As a result, the atomic number decreases by 2 and the mass number decreases by 4. 2. Beta(β−) emission: This occurs when a neutron in the nucleus is converted into a proton, emitting an electron (called a beta particle). The atomic number increases by 1, but the mass number remains unchanged. 3. Positron emission: This is similar to beta emission, but a proton is converted into a neutron, releasing a positron. The atomic number decreases by 1 and the mass number remains unchanged. 4. K-electron capture: In this process, the nucleus captures an inner shell (K-shell) electron, which combines with a proton to form a neutron. The atomic number decreases by 1, and the mass number remains unchanged. 5. Gamma decay: This involves the emission of a high-energy photon (called a gamma-ray) from an excited nucleus. There is no change in the atomic number or mass number in this process.

Filling in the Table

Now that we know how each nuclear reaction affects the atomic number and mass number, let's fill in the table: $$ \begin{array}{lcc} \text { Event } & \begin{array}{c} \text { Change in }\\\ \text { Atomic Number } \end{array} & \begin{array}{c} \text { Change in }\\\ \text { Mass Number } \end{array} \\ \hline \alpha \text { -decay } & -2 & -4 \\ \beta \text { -emission } & +1 & 0 \\ \text { positron emission } & -1 & 0 \\ \text { K-electron capture } & -1 & 0 \\ \gamma \text {-decay } & 0 & 0 & \end{array} $$ The completed table provides the required information about the change in atomic number and mass number for the given nuclear reactions. Make sure to remember how these processes affect the atoms and familiarize yourself with the changes that occur during each type of decay.

Key concepts

Alpha Decay

Alpha decay is a type of radioactive process where an unstable atom emits an alpha particle to become more stable. An alpha particle is essentially a helium nucleus, consisting of two protons and two neutrons.

When an atom undergoes alpha decay, its atomic number decreases by two because it has lost two protons, and its mass number decreases by four as it loses the entire alpha particle. This transformation leads to the formation of a new element that is two places back in the periodic table from the original one. For example, when Uranium-238 undergoes alpha decay, it transforms into Thorium-234.

Alpha particles, due to their relatively large size, have a limited ability to penetrate materials and can be stopped by a sheet of paper or the skin's outer layer.

Beta Emission

Beta emission, or beta decay, involves the transformation of a neutron into a proton while releasing an electron (called a beta particle) and an antineutrino. This conversion happens within an unstable nucleus that has an excess of neutrons.

The atomic number increases by one since a new proton is produced, nudging the element one place up in the periodic table; however, the mass number remains the same, since a neutron and a proton have nearly equal masses. For instance, Carbon-14 decays into Nitrogen-14 through beta emission.

Beta particles are more penetrating than alpha particles and can pass through a few millimeters of a substance like aluminum.

Positron Emission

Positron emission is a nuclear reaction similar to beta emission but works in reverse. A proton within the nucleus is transformed into a neutron and simultaneously, a positron (the electron's antimatter counterpart) is emitted.

This process reduces the atomic number by one since it loses a proton, but again, the mass number is unaltered due to the mass equivalence of proton and neutron. Positron emission occurs in proton-rich nuclei and leads to the conversion of one element to another located one place lower in the periodic table.

Positrons interact with electrons in a process called annihilation, where both particles are destroyed, producing gamma rays.

K-electron Capture

K-electron capture is another process that occurs in proton-rich nuclei. The nucleus absorbs one of the atom's own inner shell electrons, typically from the closest orbit, known as the K-shell. The absorbed electron combines with a proton and forms a neutron.

As a result, the atomic number decreases by one as a proton is lost, yet the mass number remains the same. Sometimes, this process is followed by X-ray emission, as other electrons rearrange to fill the vacancy left in the K-shell. K-electron capture is less common to observe compared to other forms of decay because it does not leave a directly observable track like alpha or beta particles.

Gamma Decay

Gamma decay occurs when a nucleus in an excited state (often following another decay) releases excess energy in the form of gamma rays. Gamma rays are high-energy photons, with no charge and no mass.

Different from alpha, beta, and positron emissions, gamma decay does not involve a change in the atomic number or mass number. It merely moves the nucleus from a high-energy state to a lower-energy, more stable state. Since gamma rays are very penetrating, they can pass through several centimeters of lead. Gamma decay is often observed alongside other types of decay as the nucleus seeks a more stable energetic state.