Question

Predict the type of radioactive decay process for the following radionuclides: (a) \({ }_{5}^{8} \mathrm{~B}\), (b) \({ }_{29}^{68} \mathrm{Cu}\), (c) phosphorus32, (d) chlorine-39.

Short answer

Boron-8 undergoes beta-plus decay, Copper-68 undergoes beta-minus decay, Phosphorus-32 undergoes beta-minus decay, and Chlorine-39 undergoes beta-minus decay.

Step-by-step solution

Identifying radioactive decay process for \({ }_{5}^{8} \mathrm{~B}\) (Boron-8)

To identify the decay process for Boron-8, let's first look at the nucleus. It has 5 protons and 3 neutrons (the mass number 8 minus the atomic number 5). The nucleus is very unstable, with too few neutrons to stabilize the protons. This results in the nucleus undergoing beta-plus decay, in which a proton is converted into a neutron, along with the emission of a positron and an electron neutrino. This increases the number of neutrons while decreasing the number of protons, resulting in the formation of a more stable atom.

Identifying radioactive decay process for \({ }_{29}^{68} \mathrm{Cu}\) (Copper-68)

Copper-68 has 29 protons and 39 neutrons (68 - 29). The neutrons outnumber the protons, making the nucleus unstable in this case. To achieve a more stable configuration, the nucleus will undergo beta-minus decay, during which a neutron is converted into a proton, along with the emission of an electron and an electron antineutrino. This results in the formation of a more stable atom.

Identifying radioactive decay process for Phosphorus-32

Phosphorus-32 has 15 protons and 17 neutrons (32 - 15). The neutron to proton ratio is higher than stable isotopes of phosphorus, leading to an unstable nucleus. The nucleus undergoes beta-minus decay, converting a neutron into a proton, emitting an electron and an electron antineutrino in the process. This results in a more stable atom.

Identifying radioactive decay process for Chlorine-39

Chlorine-39 has 17 protons and 22 neutrons (39 - 17). The nucleus is unstable due to the higher number of neutrons compared to protons. The nucleus will undergo beta-minus decay, converting a neutron to a proton. This process involves the emission of an electron and an electron antineutrino. The resulting atom will be more stable.

Key concepts

Beta Decay

Radioactive elements often undergo transformations to achieve greater stability. One common form of such a transformation is beta decay. In beta decay, a nucleus becomes more stable by altering its neutron-to-proton balance.
There are two types of beta decay:

• Beta-minus decay: In this type, a neutron is transformed into a proton. This process is accompanied by the emission of an electron (often referred to as a beta particle) and an electron antineutrino. This increases the atomic number by one, converting the element into a new one. For example, for Copper-68 and Phosphorus-32, the transformations result in a stabilized nucleus by increasing the number of protons.
• Beta-plus decay (or positron emission): Here, a proton is converted into a neutron. This results in the emission of a positron and an electron neutrino. The atomic number decreases by one, again transforming the element. Boron-8 is an example of beta-plus decay, adjusting the neutron-to-proton ratio favorably.

Beta decay is critical in understanding the path a radioactive element might take towards nuclear stability.

Nuclear Stability

Nuclear stability refers to how likely a nucleus is to remain unchanged over time. Unstable nuclei are prone to decay, releasing particles in the process. Several factors determine nuclear stability:

• Neutron-to-proton ratio: A balanced ratio is crucial for stability. Deviations often lead to radioactive decay as the nucleus attempts to attain a stable form.
• Magic numbers: Nuclei with a certain "magic" number of protons or neutrons are particularly stable, akin to noble gases in chemistry.

In the context of our problem, the isotopes mentioned are unstable because their neutron-to-proton ratios need adjustment. Through beta decay, these nuclei find pathways to become more stable. Understanding nuclear stability is essential for predicting the behavior of radioactive isotopes in nature.

Isotopes

Isotopes are varieties of elements that contain the same number of protons but differ in the number of neutrons. Despite sharing chemical properties, isotopes can exhibit varied nuclear properties, leading to differing stabilities.
Elements like Boron, Copper, Phosphorus, and Chlorine all possess multiple isotopes, each with unique characteristics.

• Stable isotopes: These possess neutron-to-proton ratios that do not lead to radioactive decay.
• Radioactive isotopes: Also known as radioisotopes, these isotopes are unstable and undergo radioactive decay, such as beta decay. They seek neutron-proton balance for stability, a necessity for achieving long-term existence.

A deep understanding of isotopes aids in comprehending chemical reactions and radioactive decay processes encountered in various scientific fields.

Neutron-to-Proton Ratio

An important aspect of nuclear chemistry is the neutron-to-proton ratio. It is pivotal in determining the stability of a nucleus. Protons, being positively charged, repel each other. Neutrons, which are neutral, help to create a buffer, adding to the cohesive force.

• Balanced ratio: A 1:1 ratio is typically stable for elements with low atomic numbers. As atomic number increases, more neutrons are needed for stability.
• Imbalanced ratio: When the ratio deviates significantly from the stable norm, decay processes like beta decay are triggered. This alters the ratio in pursuit of stability, rounding off excess protons or neutrons.

The isotopes mentioned, such as Boron-8, Copper-68, Phosphorus-32, and Chlorine-39, demonstrate differences in neutron-to-proton ratios that necessitate beta decay for achieving stability. Understanding these ratios is crucial for predicting the behavior of isotopes.