Chapter 25, Problem 59A

(a)

Interpretation Introduction

Interpretation:

The nuclear reaction is to be completed.

Concept Interpretation:

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Answer to Problem 59A

The balance nuclear equation is $P\to S+e$ .

Explanation of Solution

Note that the reactant's mass number is $\text{32}$ and the atomic number is $\text{15}$ . In order to complete the nuclear equation, the mass number, as well as the atomic number of the products, must be conserved. Since the unknown product combines with an electron $\text{(}\text{e}\text{)}$ , it must have a mass number of $\text{32}$ and an atomic number of $\text{16}$ . $$

The complete and balanced nuclear equation is:

  $P\to S+e$ .

Hence, the missing particle is $S$

(b)

Interpretation Introduction

Interpretation:

The nuclear reaction is to be completed.

Concept Interpretation:

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Answer to Problem 59A

  $\text{C}\to \text{N}\text{+}\text{e}$

Explanation of Solution

In order to determine the unknown isotope which is decaying, at first we must determine its atomic and mass numbers. Since an electron has no mass, the mass number stays the same, while the atomic number can be found when we subtract $\text{1}$ from the atomic number of nitrogen.

The complete and balanced nuclear equation is:

  $\text{C}\to \text{N}\text{+}\text{e}$

(c)

Interpretation Introduction

Interpretation:

The nuclear reaction is to be completed.

Concept Interpretation:

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Answer to Problem 59A

The missing elements is $He$ .

Explanation of Solution

The reactant's mass number is $238$ and the atomic number is $92$ . In order to complete the nuclear equation, the mass number, as well as the atomic number of the products, must be conserved. The unknown product must have a mass number of $4$ and an atomic number of $2$

The complete and balanced nuclear equation is:

  $U\to Th+He$ .

(d)

Interpretation Introduction

Interpretation:

The nuclear reaction is to be completed.

Concept Interpretation:

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Answer to Problem 59A

The missing elements is $La$ .

Explanation of Solution

The reactant's mass number is $141$ and the atomic number is $56$ . In order to complete the nuclear equation, the mass number, as well as the atomic number of the products, must be conserved. Since the unknown product combines with an electron $\text{e}$ , it must have a mass number of $141$ and an atomic number of $57$ .

The complete nuclear equation is:

  $Ba\to La+e$ .

(e)

Interpretation Introduction

Interpretation:

The nuclear reaction is to be completed.

Concept Interpretation:

The process of radioactive decay is how an unstable atomic nucleus loses energy through radiation. A substance that has unstable nuclei is regarded as radioactive.

Answer to Problem 59A

The missing element is $Au$ .

Explanation of Solution

In order to determine the unknown isotope which is decaying, we first must determine its atomic and mass numbers.

To write the missing symbol in the nuclear radiation, we should make sure the mass numbers and atomic numbers of the reactants sum up to the mass numbers and atomic numbers of the products.

Mass Number: $\text{181+4=185}$

Atomic number: $\text{77+2=79}$

We can find this element in the periodic system of elements by its atomic number which has a value of 79 and this isotope that decay is gold $\text{-185}$

  $Au$ .

The complete and balanced nuclear equation is:

  $\text{A}\text{u}\to \text{I}\text{r+}\text{H}\text{e}$