Problem 1 - Chemistry and Global Awareness

Question

Translate the following artificial transmutation reactions into nuclear symbols and balance: a. Be-9 is hit with an alpha particle to produce C-12 and? b. \(\mathrm{Li}-6\) is bombarded with deuterium to form ? and \(\mathrm{Li}-7\) c. A neutron hits \(\mathrm{N}-14\) to produce an alpha particle and ? d. Na-23 combines a neutron to form Na-24 and?

Step-by-Step Solution

Answer

a) Neutron (n); b) Proton (H); c) Boron-11 (B); d) Gamma photon (γ).

Step 1: Write the Given Reaction

For each artificial transmutation, start by writing down the known reactants and products. This sets the framework of the nuclear equation that needs to be balanced.

Step 2: Use Atomic and Mass Number Conservation

For each reaction, ensure that the sum of atomic numbers (protons) and the sum of mass numbers (protons and neutrons) are equal on both sides of the reaction.

Step 3a: Solve for Unknown in Reaction (a)

The reaction is: \[ ^9_4\text{Be} + ^4_2\text{He} \rightarrow ^{12}_6\text{C} + X \]Balancing mass and atomic numbers, we find:\[ Mass: 9 + 4 = 12 + A_X \Rightarrow A_X = 1 \]\[ Atomic: 4 + 2 = 6 + Z_X \Rightarrow Z_X = 0 \]The unknown particle is a neutron: \(^1_0\text{n}\).

Step 3b: Solve for Unknown in Reaction (b)

The reaction is:\[ ^6_3\text{Li} + ^2_1\text{H} \rightarrow X + ^7_3\text{Li} \]Balancing mass and atomic numbers, we find:\[ Mass: 6 + 2 = A_X + 7 \Rightarrow A_X = 1 \]\[ Atomic: 3 + 1 = Z_X + 3 \Rightarrow Z_X = 1 \]The unknown particle is a proton: \(^1_1\text{H}\).

Step 3c: Solve for Unknown in Reaction (c)

The reaction is:\[ ^1_0\text{n} + ^{14}_7\text{N} \rightarrow ^4_2\text{He} + X \]Balancing mass and atomic numbers, we find:\[ Mass: 1 + 14 = 4 + A_X \Rightarrow A_X = 11 \]\[ Atomic: 0 + 7 = 2 + Z_X \Rightarrow Z_X = 5 \]The unknown particle is boron-11: \(^{11}_5\text{B}\).

Step 3d: Solve for Unknown in Reaction (d)

The reaction is:\[ ^{23}_{11}\text{Na} + ^1_0\text{n} \rightarrow ^{24}_{11}\text{Na} + X \]Balancing mass and atomic numbers, we find:\[ Mass: 23 + 1 = 24 + A_X \Rightarrow A_X = 0 \]\[ Atomic: 11 + 0 = 11 + Z_X \Rightarrow Z_X = 0 \]The unknown particle is a gamma photon: \(^0_0\gamma\).

Key Concepts

nuclear equations

Nuclear equations represent the processes occurring in the nucleus during reactions, such as artificial transmutation. These equations are similar to chemical equations, but they focus on atomic nuclei. In nuclear equations, we account for the particles involved, like neutrons, protons, and other atomic particles.

The process involves indicating the reactants on the left side and the products on the right, separated by an arrow. Each nuclear species is represented by its nuclear symbol, a notation that includes the mass number at the top-left and the atomic number at the bottom-left of the element symbol.

• The mass number (A) is the sum of protons and neutrons in the nucleus.
• The atomic number (Z) is the number of protons.

This symbolic representation helps visualize changes in nuclear reactions and check for balance, ensuring that mass number and atomic number are conserved.

mass number conservation

Mass number conservation is crucial in nuclear equations. It states that the sum of mass numbers on the reactant side must equal the sum on the product side.

Therefore, when writing or balancing a nuclear equation, you add the mass numbers for all reactants and products. This ensures that the total number of nucleons remains constant, even as they may rearrange themselves among different nuclei.

• For example, in the equation \[ ^9_4\text{Be} + ^4_2\text{He} \rightarrow ^{12}_6\text{C} + X \]
the mass numbers 9 and 4 on the left equal the mass number 12 on the right, indicating the unknown particle must have a mass number of 1, showing mass conservation in action.

Whenever a nuclear reaction question arises, always check mass numbers first to ensure they're consistent across the equation.

atomic number conservation

Atomic number conservation is another essential principle in nuclear physics. It means the total atomic numbers on both sides of a nuclear equation should be equal.
An atomic number represents the number of protons in the nucleus, which determines the element. During nuclear reactions, the type of particles changes, but the overall balance of protons should remain the same.

• For instance, in the transmutation equation, \[ ^6_3\text{Li} + ^2_1\text{H} \rightarrow X + ^7_3\text{Li} \]
the sum of atomic numbers 3 and 1 on the left must equal the 3 on the right, implying that the missing particle must be a proton with atomic number 1.

Understanding atomic number conservation helps us identify unknown products or reactants in nuclear reactions.

neutron

Neutrons are subatomic particles with no electric charge, a key component of atomic nuclei besides protons. They influence atomic mass without altering the atomic charge.
Neutrons play a critical role in nuclear reactions and stability. They're instrumental in processes such as nuclear fission and artificial transmutation.

• Neutrons are often represented in nuclear equations by the symbol \(^1_0\text{n}\).
• They are essential in initiating changes that convert elements into different isotopes or new elements.
• For example, a neutron bombarding \( ^{14}_7\text{N} \), results in a transmutation, producing an alpha particle and another element.

Their flexibility makes neutrons valuable in nuclear reactions, as they can penetrate atomic nuclei without repulsion.

proton

Protons are positively charged particles found within atomic nuclei. The number of protons, known as the atomic number, defines the element of an atom.

In nuclear reactions, protons are crucial for balancing nuclear equations and determining elemental identity. They are denoted in nuclear notation as \(^1_1\text{H}\) due to having both one proton and a mass number of one.

• Protons can be involved in nuclear reactions, such as artificial transmutations, where they can both begin or result from the process.
• For example, in the reaction \( ^6_3\text{Li} + ^2_1\text{H} \rightarrow X + ^7_3\text{Li} \), the unknown part resolved as a proton ( \(^1_1\text{H}\)).

Understanding protons' role can illuminate how nuclear reactions transform into different elements through artificial processes.

alpha particle

An alpha particle is a type of nuclear particle consisting of two protons and two neutrons, identical to a helium nucleus (\(^4_2\text{He}\)). Alpha particles are a common product of nuclear decay processes but also play a role in artificial transmutation.

• Alpha particles can be emitted during the decay of heavy nuclei, contributing to the transformation of elements.
• They are typically denoted by either \(^4_2\text{He}\) or \(\alpha\) in nuclear equations.
• In the reaction \( ^9_4\text{Be} + ^4_2\text{He} \rightarrow ^{12}_6\text{C} + X \), an alpha particle collides with beryllium, facilitating the production of carbon-12.

Alpha particles provide a tangible way to visualize nuclear transformation, emphasizing the interactions leading to new species formation.

gamma photon

Gamma photons are electromagnetic waves of very high energy, emitted during nuclear reactions as a way of releasing excess energy. They have no mass or charge, unlike other nuclear particles such as protons or neutrons, and are simply indicated as \(^0_0\gamma\) in nuclear equations.

• Gamma photons often accompany other nuclear reactions, serving to stabilize the resulting nuclei by reducing energy.
• For instance, in the equation \( ^{23}_{11}\text{Na} + ^1_0\text{n} \rightarrow ^{24}_{11}\text{Na} + X \), the unknown particle is a gamma photon, which indicates an energy adjustment rather than a change in particle count.
• Gamma emission is invisible yet penetrates deeply, a characteristic employed in medical and industrial applications.

Understanding gamma photons aids in comprehending how nuclei adjust energy states, revealing the delicate balance in nuclear reactions.