Chapter 19, Problem 13A

(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.

Answer to Problem 13A

The balanced nuclear equation: ${}_{89}^{210}Ac\to {}_2^{4}He+{}_{87}^{206}Fr$

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,

  $\begin{array}{c}A+2=89\\ A=89-2\\ A=87\end{array}$

Atomic number 87 corresponds to Francium.

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

According to conservation of mass number,

  $\begin{array}{c}M+4=210\\ M=210-4\\ M=206\end{array}$

So, the balanced nuclear equation: ${}_{89}^{210}Ac\to {}_2^{4}He+{}_{87}^{206}Fr$

(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.

Answer to Problem 13A

The balanced nuclear equation: ${}_{53}^{131}I\to {}_{54}^{131}Xe+{}_{-1}^{0}e$

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 $=A+54$

According to conservation of atomic number,

  $\begin{array}{c}A+54=53\\ A=-1\end{array}$

So, the missing element is beta particle.

Similarly, total mass number on right side of the equation is $=M+131$

  $\begin{array}{c}M+131=131\\ M=0\end{array}$

So, the balanced nuclear equation: ${}_{53}^{131}I\to {}_{54}^{131}Xe+{}_{-1}^{0}e$

(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.

Answer to Problem 13A

The balanced nuclear equation: ${}_{35}^{88}Br\to {}_{35}^{87}\text{Br }+{}_0^{\text{1}}n$

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 $=A+35$

According to conservation of atomic number,

  $\begin{array}{c}A+35=35\\ A=0\end{array}$

Similarly, total mass number on right side of the equation is $=M+87$

  $\begin{array}{c}M+87=88\\ M=1\end{array}$

So, the missing particle is neutron. The balanced nuclear equation: ${}_{35}^{88}Br\to {}_{35}^{87}\text{Br }+{}_0^{\text{1}}n$