Problem 41 - Chemistry and Chemical Reactivity

Question

The super-heavy element \(^{2 \times 7}\) Uuq (element 114 ) was made by firing a beam of "Ca ions at \(^{242} \mathrm{Pu}\). Three neutrons were ejected in the reaction. Write a balanced nuclear equation for the synthesis of \(^{2 \pi}\) Uuq.

Step-by-Step Solution

Answer

The balanced nuclear equation is: \(^{242}_{94}\text{Pu} + ^{48}_{20}\text{Ca} \rightarrow ^{287}_{114}\text{Uuq} + 3\ ^1_0\text{n}\).

Step 1: Understand the Components

Before writing the nuclear equation, identify the elements involved and their roles. The problem involves a target of \(^{242}\text{Pu}\) (plutonium) and a projectile of \(^{48}\text{Ca}\) (calcium). The reaction produces \(^{287}\text{Uuq}\) and ejects 3 neutrons.

Step 2: Understand the Nuclear Reaction

The main idea of nuclear equation balancing is that the total number of protons and neutrons (collectively called nucleons) must remain constant. The incident nucleus combines with the target nucleus, possibly ejecting some particles (in this case, neutrons).

Step 3: Understand the Symbols

Convert the elemental symbols into their nuclear notations. Plutonium (Pu) is element number 94, so \(^{242}_{94}\text{Pu}\) is used. Calcium (Ca) is element number 20, thus \(^{48}_{20}\text{Ca}\). The resulting element is livermorium (Uuq), also known as Fl (flerovium), which is element number 114, noted as \(^{287}_{114}\text{Uuq}\).

Step 4: Set Up the Equation

Use your understanding of nuclear reactions to set up the nuclear equation. The general form is: \[\text{Target (Pu)} + \text{Projectile (Ca)} \rightarrow \text{Product (Uuq)} + \text{Ejected particles}\] Insert our values: \[^{242}_{94}\text{Pu} + ^{48}_{20}\text{Ca} \rightarrow ^{287}_{114}\text{Uuq} + 3\ ^1_0\text{n}\]

Step 5: Verify Balance in the Nuclear Equation

Add the masses and atomic numbers separately on each side of the equation to ensure balance. On the left side, the mass numbers are \(242 + 48 = 290\); on the right side, \(287 + (3 \times 1\ foreutrons) = 290\). The atomic numbers are balanced as well: \(114 = 94 + 20\). This confirms the equation is balanced.

Key Concepts

Nuclear Equation Balancing

Balancing a nuclear equation involves ensuring that the total number of protons and neutrons (nucleons) remains constant on both sides of the reaction. This is similar to balancing chemical equations, but instead of atoms and molecules, we’re dealing with atomic nuclei.

Here's a simple process:

• Identify Elements: Know the atomic number and mass number for each element involved.
• Set Up Equation: Arrange the target, projectile, resulting element, and any ejected particles.
• Check Balance: Ensure both the total mass numbers and atomic numbers are equal on each side.

For example, when balancing the equation: \(^{242}_{94}\text{Pu} + ^{48}_{20}\text{Ca} \rightarrow ^{287}_{114}\text{Uuq} + 3\ ^1_0\text{n}\), you check that the mass numbers (242 + 48 = 290) and atomic numbers (94 + 20 = 114) are equal before and after the reaction.

Super-heavy Elements

Super-heavy elements are fascinating because they are not typically found in nature and usually have a high atomic number (greater than 104). These elements, like livermorium (Uuq), are created in labs through nuclear reactions.

Some key characteristics include:

• Stability: They tend to be very unstable, decaying quickly.
• Discovery Methods: They are often synthesized by bombarding heavier targets with lighter particles.
• Research Significance: Studying them helps scientists understand nuclear forces and the limits of the periodic table.

In the given exercise, livermorium (element 114) is synthesized using plutonium and calcium ions. This involves overcoming repulsive nuclear forces to combine these nuclei, often resulting in more temporary, short-lived elements.

Neutron Ejection

In nuclear reactions, particles like neutrons may be ejected as a result of energy redistribution. It's crucial in balancing nuclear equations, as the ejection impacts the final mass and atomic numbers.

Considerations when neutrons are ejected include:

• Energy Levels: High energy collisions can cause ejection, leading to new element formation.
• Nuclear Stability: Elements may eject neutrons to achieve a more stable configuration.
• Impact on Equations: Each ejected neutron slightly alters the mass balance, as seen with the inclusion of 3 neutrons in the exercise.

For the equation \(^{242}_{94}\text{Pu} + ^{48}_{20}\text{Ca} \rightarrow ^{287}_{114}\text{Uuq} + 3\ ^1_0\text{n}\), the ejected neutrons are added to preserve balance, ensuring the equation reflects the conservation of mass and atomic numbers accurately.