Question

To synthesize the heavier transuranium elements, one must react a lighter nucleus with a relatively large particle. If you know that the products of such a reaction are californium- 246 and four neutrons, what particle must have reacted with uranium- 238 atoms?

Short answer

The particle is carbon-12.

Step-by-step solution

Identify Known Information

We know that californium-246 and four neutrons are products of the reaction. Therefore, we need to set up a nuclear equation with these products.

Set Up the Nuclear Equation

For a nuclear reaction: \[ \text{Reactants} \rightarrow \text{Products} \]. We know part of the equation: \[ \text{Uranium-238} + \text{?} \rightarrow \text{Californium-246} + 4\text{n} \].

Determine Atomic and Mass Numbers

The atomic number of uranium (U) is 92, and its mass number is 238. Californium (Cf) has an atomic number of 98 and a mass number of 246. Neutrons (n) have an atomic number of 0 and a mass number of 1. We need to add 4 neutrons: \[ 4 \times 1 = 4 \] to the equation.

Balance Mass and Atomic Numbers

Balance the equation by ensuring that the sum of atomic numbers and mass numbers of reactants equals the sum of those in the products. \[ A + 238 = 246 + 4 \] for mass numbers, and \[ Z + 92 = 98 + 0 \] for atomic numbers, where A and Z are the mass and atomic numbers of the unknown particle, respectively.

Solve for the Missing Particle

Solve the equations: \[ A + 238 = 246 + 4 \Rightarrow A = 246 + 4 - 238 = 12 \] and \[ Z + 92 = 98 \Rightarrow Z = 98 - 92 = 6 \]. The particle with atomic number 6 and mass number 12 is carbon-12.

Key concepts

Transuranium Elements

Transuranium elements are elements with atomic numbers greater than 92. This means they are heavier than uranium, the heaviest naturally occurring element on Earth. These elements are not typically found in nature; they must be synthesized in laboratories through nuclear reactions.
These elements are of great interest for various scientific and practical reasons, including their potential use in nuclear energy and research. Examples of transuranium elements include neptunium, plutonium, and californium, all of which have unique properties but require complex processes to produce.
Understanding how to create these elements involves combining existing lighter elements, such as uranium, with other particles or nuclei to make new, heavier atoms. This is done in controlled environments using particle accelerators or nuclear reactors.

Balancing Atomic and Mass Numbers

In nuclear reactions, balancing atomic and mass numbers is crucial to ensuring that the reaction adheres to the laws of conservation. This means the total mass number (representing the sum of protons and neutrons in the nucleus) and the total atomic number (showing the number of protons) must be the same on both sides of the equation.
For example, when uranium-238 is combined with a particle to produce californium-246 and four neutrons, we start by writing the known parts of the nuclear equation. We denote the unknown particle as having atomic number \( Z \) and mass number \( A \).

• The mass number equation is: \( A + 238 = 246 + 4 \)
• The atomic number equation is: \( Z + 92 = 98 \)

By solving these, we find that \( A = 12 \) and \( Z = 6 \), which corresponds to a carbon-12 nucleus, illustrating how we balance nuclear equations.

Synthesis of Heavier Elements

The synthesis of heavier elements often involves bombarding a target nucleus (such as uranium-238) with a smaller particle or nucleus. This process helps to create new, heavier elements that aren't naturally available. Bombardment reactions often use neutrons, protons, or smaller nuclei like carbon (as in our example with carbon-12).
To achieve fusion and create a new, heavier atom, high-energy conditions are essential. This is typically done in particle accelerators, where particles are accelerated to very high speeds before colliding with the target nucleus.
The goal is to overcome the electrostatic repulsion between the positively charged nuclei, so the strong nuclear force can bind them together. When successful, this process broadens our understanding of atomic nuclei and allows for the discovery of new elements, driving advancements in both theoretical and practical applications of nuclear science.