Question

Complete each of the following nuclear equations by supplying the missing particle. a. \({ }_{80}^{201} \mathrm{Hg}+{ }_{-1}^{0} \mathrm{e} \rightarrow ?\) \(\mathrm{b} . ? \rightarrow{ }_{83}^{210} \mathrm{Br}+{ }_{-1}^{0} \mathrm{e}\) c. \({ }_{83}^{210} \mathrm{Bi} \rightarrow ?_{-1}^{0} \mathrm{e}\)

Short answer

The short answers to the nuclear equations are: a. \({ }_{80}^{201} \mathrm{Hg}+{ }_{-1}^{0} \mathrm{e} \rightarrow { }_{79}^{201} \mathrm{Au}\) b. \({ }_{84}^{210} \mathrm{Po} \rightarrow{ }_{83}^{210} \mathrm{Br}+{ }_{-1}^{0} \mathrm{e}\) c. \({ }_{83}^{210} \mathrm{Bi} \rightarrow { }_{84}^{210} \mathrm{Po} +{ }_{-1}^{0} \mathrm{e}\)

Step-by-step solution

Equation (a)

Given: \({ }_{80}^{201} \mathrm{Hg}+{ }_{-1}^{0} \mathrm{e} \rightarrow ?\) Apply the conservation of mass number (A) and atomic number (Z) to find the missing particle: A conservation: 201 (Hg) + 0 (e) = A (Missing particle) Z conservation: 80 (Hg) - 1 (e) = Z (Missing particle) Now we can find the missing particle: A (Missing particle) = 201 Z (Missing particle) = 79 The missing particle is: \({ }_{79}^{201} \mathrm{Au}\)

Equation (b)

Given: \(? \rightarrow{ }_{83}^{210} \mathrm{Br}+{ }_{-1}^{0} \mathrm{e}\) Apply the conservation of mass number (A) and atomic number (Z) to find the missing particle: A conservation: A (Missing particle) = 210 (Br) + 0 (e) Z conservation: Z (Missing particle) = 83 (Br) - 1 (e) Now we can find the missing particle: A (Missing particle) = 210 Z (Missing particle) = 84 The missing particle is: \({ }_{84}^{210} \mathrm{Po}\)

Equation (c)

Given: \({ }_{83}^{210} \mathrm{Bi} \rightarrow ?_{-1}^{0} \mathrm{e}\) Apply the conservation of mass number (A) and atomic number (Z) to find the missing particle: A conservation: 210 (Bi) = A (Missing particle) + 0 (e) Z conservation: 83 (Bi) = Z (Missing particle) - 1 (e) Now we can find the missing particle: A (Missing particle) = 210 Z (Missing particle) = 84 The missing particle is: \({ }_{84}^{210} \mathrm{Po}\)

Key concepts

Nuclear Chemistry

Nuclear chemistry is a fascinating branch of chemistry that deals with reactions and changes involving the nuclei of atoms. Unlike traditional chemistry that involves electrons and their arrangements during chemical reactions, nuclear chemistry focuses on phenomena such as radioactive decay, nuclear fission, and nuclear fusion. These processes can alter the identity of atoms significantly by changing their atomic number, which defines the element, or their mass number, which represents the total number of protons and neutrons in the nucleus.

For students to understand nuclear chemistry, it's crucial to grasp the concept of nuclear stability and what leads to nuclear reactions. This understanding can help solve exercises dealing with nuclear equations, where the objective is to identify unknown particles by applying conservation laws. These nuclear equations illustrate the transformation of one nucleus into another and allow us to predict the products of nuclear reactions.

Conservation of Mass Number

The conservation of mass number is a fundamental principle in nuclear chemistry. It indicates that during a nuclear reaction, the sum of the mass numbers of reactants (the total number of protons and neutrons) must equal the sum of the mass numbers of the products. This principle is critical when solving nuclear equations because it lets you balance the equation effectively to predict missing components. For example, in a nuclear equation, if the mass number of one side is known, you can apply the conservation principle to calculate the corresponding mass number on the other side.

Understanding how to apply the conservation of mass number is vital. It allows us to keep track of nucleons, which are the particles (protons and neutrons) found within the nucleus of an atom. After understanding this concept, students can effortlessly find missing particles in nuclear equations, such as in the exercise provided, simply by ensuring that the total mass number remains constant before and after the reaction.

Conservation of Atomic Number

The conservation of atomic number is another pivotal principle that underpins nuclear chemistry. It states that the sum of atomic numbers, which are equivalent to the number of protons in the nucleus, must remain unchanged over the course of a nuclear reaction. This means that the total charge is conserved; hence the identity of an element can be tracked throughout the reaction. This conservation is crucial when filling in nuclear equations as it ensures elements on both sides of the reaction are balanced.

When students work on nuclear equations, recognizing this conservation law allows them to identify which element is involved in the reaction based on its atomic number. The atomic number uniquely defines an element on the periodic table, and its conservation ensures that an element can change into another through nuclear reactions. For instance, identifying a wire particle with a known atomic number but an unknown element requires understanding that the number of protons defines the element, which can be derived using this conservation law, as shown in the step-by-step solution for the exercise.