Question

The nuclear fusion of a lithium- 7 nucleus and particle \(X\) releases two alpha particles and a neutron. Identify particle X.

Short answer

Particle X is Deuterium, \(^2_1 \text{H}\).

Step-by-step solution

Write the given nuclear reaction

The nuclear fusion reaction involves:\[ \text{Li-7} + X \rightarrow 2 \ \alpha \text{ particles} + n \]where Li-7 is a Lithium-7 nucleus, \(\alpha\) particles are helium nuclei \( \text{Name - } ^4_2 \text{He} \), and \(n\) is a neutron \( ^1_0 \text{n} \).

Analyze charge and mass numbers

The Lithium-7 nucleus, \( ^7_3 \text{Li} \), has a mass number of 7 and an atomic number of 3. An \( \alpha \) particle has a mass number of 4 and an atomic number of 2. A neutron has a mass number of 1 and an atomic number of 0.

Arrange knowns to find the unknown

Applying conservation of mass number and atomic number:1. **Conservation of Mass Number:** The total mass number before and after must be equal. \[ 7 + A = 2 \times 4 + 1 \] where \( A \) is the mass number of particle X. This simplifies to: \[ 7 + A = 8 + 1 \rightarrow 7 + A = 9 \] Therefore: \[ A = 9 - 7 = 2 \]2. **Conservation of Atomic Number:** The total atomic number before and after must be equal. \[ 3 + Z = 2 \times 2 + 0 \] where \( Z \) is the atomic number of particle X. Simplifying, we find: \[ 3 + Z = 4 \] Therefore: \[ Z = 4 - 3 = 1 \]

Identify particle X

The calculated mass number of particle X is 2 and the atomic number is 1. These numbers correspond to the isotope of Hydrogen known as Deuterium, denoted \( ^2_1 \text{H} \).

Key concepts

Lithium-7 nucleus

The Lithium-7 nucleus, noted as \(^7_3 \text{Li}\), is a common isotope of lithium. Lithium is a soft, silver-white metal and the third element on the periodic table. This means it has an atomic number of 3, representing three protons in its nucleus.

The mass number of Lithium-7 is 7. This value is the sum of protons and neutrons in its nucleus. For Lithium-7, it consists of 3 protons and 4 neutrons (as 7 - 3 = 4). This isotope plays a significant role in nuclear reactions, especially in processes like nuclear fusion.

• The atomic number is always equal to the number of protons.
• The mass number is the sum of protons and neutrons.

In nuclear fusion, the Lithium-7 nucleus can react in exciting ways, releasing energy and forming different particles.

Alpha particles

Alpha particles, represented as \(^4_2 \text{He}\), are essentially helium nuclei. They consist of 2 protons and 2 neutrons, hence their atomic number is 2 and mass number is 4.

During nuclear reactions, particularly fusion, alpha particles are often produced. They carry a double positive charge due to the absence of electrons.

• Alpha particles are quite stable.
• After being emitted, they slow down by interacting with matter.
• Eventually, they can capture two electrons to become helium gas.

The production of alpha particles in nuclear fusion is significant because it points to the transformation process of original elements to new products with released energy.

Neutron

Neutrons are neutral particles found in the nucleus of an atom, denoted as \(^1_0 \text{n}\). They do not have an electric charge, which means they are neutral.

The mass number of a neutron is 1. In nuclear reactions, neutrons play a crucial role as they help stabilize the nucleus. This lack of charge allows them to penetrate atomic nuclei easily, facilitating nuclear processes like fusion.

• Neutrons can initiate reactions without being repelled or attracted by charged particles.
• They are vital in making nuclear chain reactions occur.
• In the given problem, a neutron is released as part of the nuclear fusion.

The release of a neutron in such reactions can have implications for creating new elements or isotopes.

Conservation of Mass Number

The principle of Conservation of Mass Number is fundamental in nuclear reactions. This law dictates that the total mass number before and after a nuclear reaction remains constant.

In the given nuclear fusion equation: \[ ^7_3 \text{Li} + X \rightarrow 2 \ \text{He} + \text{n} \]We apply this rule to ensure mass numbers add up correctly: \(7 + A = 8 + 1\).

• This ensures mass is neither created nor destroyed in the reaction.
• The mass number must still match the initial total mass number.

With this method, we solve for unknown particles by ensuring the laws of physics are obeyed.

Deuterium

Deuterium, symbolized as \(^2_1 \text{H}\), is also referred to as heavy hydrogen. It consists of one proton and one neutron in its nucleus.

Deuterium is an isotope of hydrogen and plays a crucial role in both nuclear fusion and various scientific processes. Its atomic number is 1 and mass number is 2.

• Deuterium combines with other nuclei in many fusion reactions.
• It is essential for producing energy in fusion reactors.

In our solved problem, deuterium was identified as the mysterious particle \(X\) due to its mass and atomic numbers fitting seamlessly into the fusion equation.

Conservation of Atomic Number

Similar to conservation of mass number, conservation of atomic number ensures that the total number of protons remains unchanged during a nuclear reaction.

In nuclear equations, this principle guarantees that atomic consistency is maintained. In the given fusion reaction:\[3 + Z = 4\].
This means that the total atomic number before the reaction must equal that after the reaction.

• This rule helps identify unknown particles involved in the reaction.
• Atomic numbers must match to balance the reaction equation.

Applying this rule enables us to find the exact properties of the nucleus participating in the process, like how particle \(X\) was determined to be Deuterium based on its atomic number.