Question

Complete the following nuclear equations. (a) \(\frac{23}{11} \mathrm{Na}+? \longrightarrow_{11}^{24} \mathrm{Na}+_{1}^{1} \mathrm{H}\) (b) \(_{27}^{59} \mathrm{Co}+_{0}^{1} \mathrm{n} \longrightarrow_{25}^{56} \mathrm{Mn}+?\) (c) \(?+_{1}^{2} \mathrm{H} \longrightarrow_{94}^{240} \mathrm{Pu}+_{-1}^{0} \beta\) (d) \(^{246} \mathrm{Cm}+? \longrightarrow_{102}^{254} \mathrm{No}+5_{0}^{1} \mathrm{n}\) (e) \(^{238} \mathrm{U}+? \longrightarrow_{99}^{246} \mathrm{Es}+6 \frac{1}{0} \mathrm{n}\)

Short answer

The unknown particles are: (a) a neutron; (b) an alpha particle ; (c) a Neptunium atom. Equations (d) and (e) appear to be incorrect as they don't satisfy conservation laws.

Step-by-step solution

Understand mass and atomic number conservation

In any given nuclear reaction, the total atomic number (also known as the charge) and the total mass number (number of protons + neutrons) are both conserved. This means the sum of atomic numbers and mass numbers on one side of the equation should equal the sum on the other side.

Apply these principles to each equation

(a) The unknown particle will have a mass number of \((24 - 23) = 1\) and an atomic number of \(11 - 11 = 0\), so it's a neutron, denoted as \(_{0}^{1}\mathrm{n}\). (b) The unknown particle will have a mass number of \((59 - 56) = 3\) and an atomic number of \(27 - 25 = 2\), so it's an alpha particle, denoted as \(_{2}^{4}\mathrm{He} \).(c) The unknown particle will have a mass number of \((240 - 2) = 238\) and an atomic number of \(94 - 1 = 93\), so it's a Neptunium atom, denoted as \(_{93}^{238}\mathrm{Np}\).(d) The unknown particle will have a mass number of \((246 - 254 + 5) = -3\) and an atomic number of \(96 - 102 = -6\), which isn't possible, indicating an error in the equation. (e) The unknown particle will have a mass number of \((238 - 246 + 6*1) = -2\) and an atomic number of \(92 - 99 = -7\), which isn't possible, indicating an error in the equation.

Summary

In this exercise, atomic and mass number conservation was used to identify unknown particles in nuclear equations. In equations (d) and (e), the conservation laws weren't followed, indicating errors in the equations.

Key concepts

Mass Number Conservation

In nuclear reactions, mass number conservation is a fundamental concept. It ensures that the total number of protons and neutrons remains the same before and after a reaction. This conservation law is applied by adding up the mass numbers on each side of the nuclear equation. The sum should be equal. For example:

• When a nucleus splits, the total mass of the resulting particles equals the mass of the original nucleus.
• In equation (a), the mass number before the reaction is 23, and it must equal 24 on the other side. By subtracting, we know the missing particle must have a mass number of 1, indicating a neutron.

Mass number is crucial because it reflects the total nucleons in the nucleus. This number helps chemists and physicists predict the products of nuclear reactions correctly.

Atomic Number Conservation

Atomic number conservation ensures that the charge remains balanced during nuclear reactions. The atomic number represents the number of protons, which determines the element's identity. Just like the mass number, the total atomic numbers on both sides of the equation must sum to the same value. Here’s how it works:

• In equation (b), the atomic number reduces from 27 to 25, requiring an additional 2 units on the other side to balance, provided by an alpha particle \(_{2}^{4}\mathrm{He} \).
• The missing particle must correct any imbalance in nuclear charge, ensuring that the type of elements involved in the reaction is conserved.

Understanding this law helps ascertain the types of particles or radiation released during nuclear transformations, making it essential for safe applications in medicine and energy.

Nuclear Reactions

Nuclear reactions involve changes in an atom's nucleus and can release or absorb a significant amount of energy. Unlike chemical reactions, nuclear reactions can transform elements into different elements by altering their nuclei. Two key types are:

• Fission: A heavy nucleus splits into two or more lighter nuclei, releasing energy.
• Fusion: Light nuclei combine to form a heavier nucleus, also releasing energy.

In the provided equations, reactions involve the transformation of elements. For instance, incoming neutrons or emitted particles alter the nucleus's structure. It's vital to follow conservation laws to correctly predict the products, as seen in exercises where balancing errors indicated mistakes. Understanding nuclear reactions is crucial for diverse fields such as energy production, where reactions power nuclear plants, and in medicine, where they are used in cancer treatments.