Problem 28 - Chemistry The Science in Context

Question

Predict the mode(s) of decay of the following radionuclides: (a) \(^{24} \mathrm{Ne} ;\) (b) \(^{38} \mathrm{K} ;(\mathrm{c})^{45} \mathrm{Ti} ;(\mathrm{d})^{237} \mathrm{Np}\)

Step-by-Step Solution

Answer

Answer: The predicted decay modes for the given radionuclides are: (a) \(^{24}\mathrm{Ne}\): Beta-minus decay (b) \(^{38}\mathrm{K}\): Beta-plus decay and/or electron capture (c) \(^{45}\mathrm{Ti}\): Beta-minus decay (d) \(^{237}\mathrm{Np}\): Alpha decay

Step 1: List the radionuclides with their mass and atomic numbers

We are given four radionuclides to predict their decay mode(s). First, we will list them with their mass numbers (A) and atomic numbers (Z): (a) \(^{24}\mathrm{Ne}\): A = 24, Z = 10 (b) \(^{38}\mathrm{K}\): A = 38, Z = 19 (c) \(^{45}\mathrm{Ti}\): A = 45, Z = 22 (d) \(^{237}\mathrm{Np}\): A = 237, Z = 93

Step 2: Analyze the radionuclides according to the Nuclear Stability Chart

We will now look at each radionuclide and evaluate its stability based on the Nuclear Stability Chart. We will use the mass and atomic numbers to determine whether the nucleus has too many protons, too many neutrons, or a balance between them. (a) \(^{24}\mathrm{Ne}\): A neutron-rich nucleus, with more neutrons than protons for its atomic number. (b) \(^{38}\mathrm{K}\): A proton-rich nucleus, with more protons than neutrons for its atomic number. (c) \(^{45}\mathrm{Ti}\): Close to the line of stability but slightly neutron-rich. (d) \(^{237}\mathrm{Np}\): A heavy nucleus, with a high atomic number (Z > 82).

Step 3: Determine the decay mode(s) based on stability

For each radionuclide, we will now predict its decay mode based on the type of instability it exhibits: (a) \(^{24}\mathrm{Ne}\): Neutron-rich nuclei tend to decay via beta-minus decay, turning a neutron into a proton. Prediction: Beta-minus decay. (b) \(^{38}\mathrm{K}\): Proton-rich nuclei can decay via beta-plus decay (turning a proton into a neutron) or electron capture (an electron is captured by a proton, thus converting it into a neutron). Prediction: Beta-plus decay and/or electron capture. (c) \(^{45}\mathrm{Ti}\): Neutron-rich but close to the line of stability; most likely, it will decay via beta-minus decay. Prediction: Beta-minus decay. (d) \(^{237}\mathrm{Np}\): Heavy nuclei typically decay via alpha decay, releasing alpha particles (helium nuclei). Prediction: Alpha decay.

Step 4: Summary of predicted decay modes

In summary, we predict the following decay modes for each radionuclide: (a) \(^{24}\mathrm{Ne}\): Beta-minus decay (b) \(^{38}\mathrm{K}\): Beta-plus decay and/or electron capture (c) \(^{45}\mathrm{Ti}\): Beta-minus decay (d) \(^{237}\mathrm{Np}\): Alpha decay

Key Concepts

Nuclear Stability

Nuclear stability refers to how likely an atomic nucleus is to stay intact without undergoing decay. This stability is determined by the ratio of neutrons to protons within the nucleus. For a nucleus to be stable, it generally needs a balanced ratio of these particles.

• Nuclei with too many neutrons compared to protons, or vice versa, often undergo radioactive decay to reach stability.
• Elements with atomic numbers greater than 82 are generally unstable because they are too heavy.

The chart known as the Nuclear Stability Chart helps in predicting whether a particular isotope will be stable or unstable and what type of decay it might undergo to reach a stable state.

Beta-Minus Decay

Beta-minus decay is a common type of radioactive decay for neutron-rich isotopes. In this process, a neutron is transformed into a proton, which increases the atomic number by one while the mass number remains unchanged.

• This process emits an electron, known as a beta particle, and an antineutrino.
• Beta-minus decay helps neutron-rich isotopes move toward stability by balancing the neutron-to-proton ratio.

A classic example of beta-minus decay can be found in the decay of neon-24, which decreases its neutron surplus by turning a neutron into a proton.

Alpha Decay

Alpha decay is a type of radioactive decay that occurs mainly in heavy nuclei with atomic numbers greater than 82. In alpha decay, the nucleus ejects an alpha particle, which consists of two protons and two neutrons, effectively reducing its atomic mass by 4 units and atomic number by 2 units.

• This type of decay helps reduce the size and energy of a heavy, unstable nucleus.
• It is quite common among heavy elements such as uranium, thorium, and neptunium.

For instance, neptunium-237 undergoes alpha decay, losing a helium nucleus and becoming a more stable nucleus.

Electron Capture

Electron capture is a unique type of decay where an electron from an atom's inner shell is captured by the nucleus. This process changes a proton into a neutron, thus decreasing the atomic number by one while leaving the mass number unchanged.

• Electron capture is common among proton-rich nuclei that are closer to achieving stability by decreasing their excess protons.
• This process often occurs in competition with another mode of decay known as beta-plus decay.

An example of electron capture can be observed in potassium-38, which might capture an electron resulting in a decrease in its proton count, helping the nucleus to stabilize.