Question

Scientists from Dubna, Russia, observed the existence of elements 118 and 116 at the Joint Institute for Nuclear Research U400 cyclotron in 2005. This was the result of bombarding calcium- 48 ions on a californium-249 target. Write a complete nuclear equation for this reaction.

Short answer

Therefore, the nuclear equation for the reaction is: \(_{20}^{48}\)Ca + \(_{98}^{249}\)Cf --> \(_{118}^{293}\)Uuo + \(_{0}^{4}\)n

Step-by-step solution

Identify the reactants

In a nuclear reaction, the reactants are the atomic nuclei that are being fused or split. In this case, we have a calcium-48 ion (expressed as \(_{20}^{48}\)Ca) and californium-249 (expressed as \(_{98}^{249}\)Cf).

Identify the products

The products of this nuclear reaction are the new elements formed, in this case, elements 118 and 116. In nuclear reactions, these elements are often referred to as the daughter nuclei.

Write the nuclear equation

The equation for a nuclear reaction shows the reactants on the left side and the products on the right side of an arrow ('-->'). The sums of the atomic and mass numbers must be equal on both sides of the equation. Therefore, the nuclear equation in this case is: \(_{20}^{48}\)Ca + \(_{98}^{249}\)Cf --> \(_{118}^{293}\)Uuo + \(_{0}^{4}\)n

Verification

Verify the correctness of the nuclear equation by checking if the atomic and mass numbers are conserved. One can verify this by adding up the atomic and mass numbers on both sides of the equation. This should result in the same two numbers: 118 and 297 for atomic and mass numbers, respectively.

Key concepts

Nuclear Reaction

A nuclear reaction is a process where the nucleus of an atom interacts with another nucleus or particle, resulting in the change of at least one nuclide. Unlike chemical reactions that involve the exchange of electrons, nuclear reactions alter the protons and neutrons in an atom's nucleus. This process can release or absorb a significant amount of energy. For instance, fusing two nuclei together or splitting a heavy nucleus into smaller parts can power stars or be harnessed for human use in nuclear power plants or weapons. A balanced nuclear equation is crucial as it represents the law of conservation of mass and charge where the sum of mass numbers (total number of protons and neutrons) and atomic numbers (protons) must be equal on both sides of the reaction. An example is the synthesis of new elements where intense energy and specific target nuclei often lead to the creation of previously unknown elements.

Atomic Number

The atomic number, symbolized as Z, is the number of protons found within the nucleus of an atom and defines the chemical identity of the element. For example, hydrogen has an atomic number of 1, meaning it has one proton in its nucleus. It is also the determining factor in the arrangement of the periodic table as elements are ordered by increasing atomic numbers. From the standpoint of a nuclear reaction, maintaining the balance of atomic numbers on either side of the equation helps ensure charge conservation. It’s essential for students to recognize that the atomic number uniquely represents each element and is what changes during the process of radioactive decay when one element transforms into another.

Mass Number

The mass number, symbolized as A, is the total number of protons and neutrons in the nucleus of an atom. Unlike the atomic number, the mass number is not the same for all atoms of an element due to the presence of isotopes—atoms of the same element with different numbers of neutrons. The mass number is significant in nuclear equations as it provides a way to calculate the relative atomic mass of a nucleus and helps ensure mass conservation during a reaction. A student analyzing a nuclear equation should check that the sum of the reactants' mass numbers equals the sum of the products' mass numbers, which indicates that nuclear reactions follow the law of conservation of mass.

Transuranium Elements

The creation and identification of transuranium elements, which are chemical elements with atomic numbers greater than 92 (the atomic number of uranium), is an exciting area of nuclear chemistry. Due to their unstable nature, these elements cannot be found naturally and are synthesized in nuclear reactors or particle accelerators, as seen in the exercise involving elements 118 and 116. Advanced nuclear reactions involving the collision of lighter elements with heavy target nuclei pave the way for scientists to discover these synthetic elements. It's important to point out that these elements are radioactively unstable and decay quickly, providing a challenge for scientists to detect and study them before they transform into different elements.