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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

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).

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.

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