Chapter 19, Problem 15A

(a)

Interpretation Introduction

Interpretation: The given equation for nuclear reaction needs to be balanced.

Concept Introduction: Nuclear reactions can be expressed similarly to that of chemical equations. The transformations of particles follow certain conservation laws. In balance a nuclear equation, the atomic numbers and mass number of all species on either side of the arrow must be equal.

Mass number and proton number of alpha particle is 4 and 2 respectively.

Answer to Problem 15A

The balanced nuclear equation: ${}_{\text{ 88}}^{226}Ra\to {}_{\text{ 86}}^{222}Rn+{}_2^{\text{4}}He$

Explanation of Solution

Let the atomic numbers and mass number of the missing element is $A$ and $M$ .

Total atomic number on right side of the equation is $=A+2$

According to conservation of atomic number,

  $\begin{array}{c}A+2=88\\ A=88-2\\ A=86\end{array}$

Atomic number 86 corresponds to Radium.

Similarly, total mass number on right side of the equation is $=M+4$

  $\begin{array}{c}M+4=226\\ M=226-4\\ M=222\end{array}$

The balanced nuclear equation: ${}_{\text{ 88}}^{226}Ra\to {}_{\text{ 86}}^{222}Rn+{}_2^{\text{4}}He$

(b)

Interpretation Introduction

Interpretation: The given equation for nuclear reaction needs to be balanced.

Concept Introduction: Nuclear reactions can be expressed similarly to that of chemical equations. The transformations of particles follow certain conservation laws. In balance a nuclear equation, the atomic numbers and mass number of all species on either side of the arrow must be equal.

Mass number and proton number of alpha particle is 4 and 2 respectively.

Answer to Problem 15A

The balanced nuclear equation: ${}_{\text{ 86}}^{222}Rn\to {}_{\text{ 84}}^{218}Po+{}_2^{\text{4}}He$

Explanation of Solution

Let the atomic numbers and mass number of the missing element is $A$ and $M$ .

Total atomic number on right side of the equation is $=A+2$

According to conservation of atomic number,

  $\begin{array}{c}A+2=86\\ A=86-2\\ A=84\end{array}$

Atomic number 84 corresponds to Polonium.

Similarly, total mass number on right side of the equation is $=M+4$

  $\begin{array}{c}M+4=222\\ M=222-4\\ M=218\end{array}$

The balanced nuclear equation: ${}_{\text{ 86}}^{222}Rn\to {}_{\text{ 84}}^{218}Po+{}_2^{\text{4}}He$

(c)

Interpretation Introduction

Interpretation: The given equation for nuclear reaction needs to be balanced.

Concept Introduction: Nuclear reactions can be expressed similarly to that of chemical equations. The transformations of particles follow certain conservation laws. In balance a nuclear equation, the atomic numbers and mass number of all species on either side of the arrow must be equal.

Mass number and proton number of alpha particle is 4 and 2 respectively.

Answer to Problem 15A

The balanced nuclear equation: ${}_{\text{ 94}}^{239}Pu\to {}_{\text{ 92}}^{235}U+{}_2^{\text{4}}He$

Explanation of Solution

Let the atomic numbers and mass number of the missing element is $A$ and $M$ .

Total atomic number on right side of the equation is $=A+2$

According to conservation of atomic number,

  $\begin{array}{c}A+2=94\\ A=94-2\\ A=92\end{array}$

Atomic number 92 corresponds to Uranium.

Similarly, total mass number on right side of the equation is $=M+4$

  $\begin{array}{c}M+4=239\\ M=239-4\\ M=235\end{array}$

The balanced nuclear equation: ${}_{\text{ 94}}^{239}Pu\to {}_{\text{ 92}}^{235}U+{}_2^{\text{4}}He$

(d)

Interpretation Introduction

Interpretation: The given equation for nuclear reaction needs to be balanced.

Concept Introduction: Nuclear reactions can be expressed similarly to that of chemical equations. The transformations of particles follow certain conservation laws. In balance a nuclear equation, the atomic numbers and mass number of all species on either side of the arrow must be equal.

Mass number and proton number of alpha particle is 4 and 2 respectively.

Answer to Problem 15A

The balanced nuclear equation: ${}_{\text{ 4}}^{8}Be\to {}_2^{\text{4}}He+{}_2^{\text{4}}He{\text{ or }}_{\text{ 4}}^{8}Be\to {\text{ 2}}_2^{\text{4}}He$

Explanation of Solution

Let the atomic numbers and mass number of the missing element is $A$ and $M$ .

Total atomic number on right side of the equation is $=A+2$

According to conservation of atomic number,

  $\begin{array}{c}A+2=4\\ A=4-2\\ A=2\end{array}$

Atomic number 2 corresponds to Helium.

Similarly, total mass number on right side of the equation is $=M+4$

  $\begin{array}{c}M+4=8\\ M=8-4\\ M=4\end{array}$

The balanced nuclear equation: ${}_{\text{ 4}}^{8}Be\to {}_2^{\text{4}}He+{}_2^{\text{4}}He{\text{ or }}_{\text{ 4}}^{8}Be\to {\text{ 2}}_2^{\text{4}}He$