Elements \(104,105,\) and 106 have been named rutherfordium (Rf), dubnium (Db), and seaborgium (Sg), respectively. These elements are synthesized from californium- 249 by bombarding with carbon-12, nitrogen-15, and oxygen-18 nuclei, respectively. Four neutrons are formed in each reaction as well. (a) Write balanced nuclear equations for the formation of these elements. (b) Write the equations in shorthand notation.

Nuclear reaction equations are a way to represent how atomic nuclei collide and transform into new atoms. These reactions often involve a projectile (like a smaller nucleus) striking a target nucleus, resulting in the formation of a new nucleus and other particles. To write these equations correctly, we need to ensure both the atomic numbers (protons) and mass numbers (protons + neutrons) balance on both sides of the equation. For instance, in the exercise, Californium-249 is bombarded with smaller nuclei like Carbon-12, Nitrogen-15, and Oxygen-18. Each reaction produces four neutrons as a byproduct. It's essential to represent this accurately both in standard notation and shorthand notation.

Element synthesis in nuclear physics involves creating new elements, often those not naturally occurring on Earth, by manipulating atomic nuclei. Scientists achieve this by bombarding stable target nuclei with smaller projectiles such as other atomic nuclei. In our exercise, elements Rutherfordium (Rf), Dubnium (Db), and Seaborgium (Sg) are synthesized. To make Rutherfordium-261, Californium-249 is hit with Carbon-12. Similarly, Dubnium-263 and Seaborgium-267 are created using Californium-249 with Nitrogen-15 and Oxygen-18, respectively. Each synthesis equation must balance in terms of both mass number and atomic number, ensuring no matter or charge is lost or gained in the process.

Nuclear physics is the study of atomic nuclei, their constituents, and interactions. It deals with the forces that hold the nucleus together (primarily the strong nuclear force) and the processes by which nuclei change (radioactive decay, fusion, and fission). In synthesizing new elements, nuclear physicists employ techniques like particle accelerators to propel nuclei at high velocities to overcome repulsive electric forces and achieve a nuclear reaction. The understanding of each interaction, energy balance, and output particles is critical. In the context of the exercise, understanding how Californium interacts with Carbon, Nitrogen, and Oxygen nuclei and how new elements and neutrons are formed provides a practical application of nuclear physics principles.