Problem 63 - Chemistry A Molecular Approach

Question

Rutherfordium-257 was synthesized by bombarding Cf-249 with C-12. Write the nuclear equation for this reaction.

Step-by-Step Solution

Answer

The balanced nuclear equation is \(_{98}^{249}\text{Cf} \) + \(_{6}^{12}\text{C} \) \(\rightarrow\) \(_{104}^{257}\text{Rf} \) + 3 \(_{0}^{1}\text{n} \).

Step 1: Identify the Reactants

Start by identifying the reactants involved in the reaction. Californium (Cf) has an atomic number of 98 and a mass number of 249, represented as \(_{98}^{249}\text{Cf} \) Carbon (C) has an atomic number of 6 and a mass number of 12, represented as \(_{6}^{12}\text{C} \)

Step 2: Identify the Product

Rutherfordium-257 is the product, with an atomic number of 104 (as per the periodic table) and a mass number of 257, which is represented as \(_{104}^{257}\text{Rf} \). Since this is a synthesis reaction, we expect the atomic numbers and mass numbers of the reactants to add up to those of the product.

Step 3: Write the Nuclear Reaction

Add the reactants on the left side of the equation, and the product on the right side. Make sure to balance the atomic numbers (protons) and mass numbers (nucleons - protons and neutrons) on both sides. The balanced nuclear equation is: \(_{98}^{249}\text{Cf} \) + \(_{6}^{12}\text{C} \) \(\rightarrow\) \(_{104}^{257}\text{Rf} \) + 3 \(_{0}^{1}\text{n} \)

Step 4: Account for the Discrepancy in Mass Numbers

After the initial addition of mass numbers (249 from Cf and 12 from C), we get a total of 261. However, the product has a mass number of 257. This means that there are excess neutrons which are accounted for as additional products in the reaction. The difference is 4, which is balanced by the presence of 3 neutrons ( 3 \times \(_{0}^{1}\text{n} \) ) on the product side.

Key Concepts

Nuclear Chemistry

Nuclear chemistry focuses on the interactions and transformations of atomic nuclei. It is a fascinating and intricate field that involves understanding the processes that power the sun, the mechanisms behind nuclear reactors, and how elements are formed within stars.
In nuclear reactions, like the one where Rutherfordium-257 is synthesized by bombarding Californium-249 with Carbon-12, the focus is on changes to the nucleus itself, different from chemical reactions which involve the exchange or sharing of electrons.
A crucial aspect in the study of nuclear chemistry is the stability of atoms. Elements with higher atomic numbers, typically above uranium in the periodic table, do not exist naturally and are synthesized in laboratories through nuclear reactions. These synthetic elements often have very short half-lives, decaying into more stable forms. Understanding the underlying principles of these processes is essential for advancements in medicine, energy, and various fields where radioactive isotopes are used.

Balancing Nuclear Equations

Balancing nuclear equations is a task that requires the conservation of mass and charge. This is crucial to ensure that the equation represents a physically possible process.
In a nuclear reaction equation, the total number of protons and neutrons - collectively known as nucleons - must be the same on both sides of the equation. Similarly, the total charge, determined by the number of protons, must remain consistent. When balancing the equation for the synthesis of Rutherfordium-257, for example, it's important to consider all of the reactants and products to maintain these balances.

• First, add up the total mass numbers (A, representing protons and neutrons) and atomic numbers (Z, representing protons) for the reactants.
• Repeat this process for the products.
• Include any additional products, such as neutrons or protons, needed to balance the mass and charge.

This careful accounting ensures that the equation is reflective of a process that adheres to the fundamental laws of physics.

Nucleon Conservation

Nucleon conservation is a principle stating that the total count of nucleons - protons and neutrons in the nucleus - must remain the same before and after a nuclear reaction. Nucleons are held together by the strong nuclear force, which is much stronger than the electromagnetic force that governs chemical reactions.
During nuclear reactions, such as the one used to synthesize Rutherfordium-257, no nucleons are lost; they are simply rearranged. Discrepancies in the count, as shown in the step-by-step solution of the synthesis reaction, are usually balanced with the emission or absorption of neutrons or other smaller particles like protons or alpha particles.
➡ For instance, the disparity between the sum of the reactants' mass numbers (249 from Californium-249 and 12 from Carbon-12, totaling 261) and the mass number of the product Rutherfordium-257 (which is 257) is balanced by the ejection of neutrons. In this case, three neutrons are emitted to conserve the total number of nucleons. Such attention to detail in nucleon conservation helps ensure the accurate depiction of nuclear reactions.