Chapter 19, Problem 52A

(a)

Interpretation Introduction

Interpretation: The given reaction needs to be balanced by supplying the missing particle.

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 52A

The balanced nuclear equation: $U\to He+Th$

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,

  $\begin{array}{c}A+2=92\\ A=92-2\\ A=90\end{array}$

Atomic number 90 corresponds to Thorium.

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

According to conservation of mass number,

  $\begin{array}{c}M+4=238\\ M=238-4\\ M=234\end{array}$

So, the balanced nuclear equation: $U\to He+Th$

(b)

Interpretation: The given reaction needs to be balanced by supplying the missing particle.

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.

The balanced nuclear equation: $Th\to Pa+e$

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 $=A+91$

According to conservation of atomic number,

  $\begin{array}{c}A+91=90\\ A=90-91\\ A=-1\end{array}$

So, the missing element is beta particle.

Similarly, total mass number on right side of the equation is $=M+234$

  $\begin{array}{c}M+234=234\\ M=234-234\\ M=0\end{array}$

So, the balanced nuclear equation: $Th\to Pa+e$

(b)

Interpretation Introduction

Interpretation: The given reaction needs to be balanced by supplying the missing particle.

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 52A

The balanced nuclear equation: $Th\to Pa+e$

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 $=A+91$

According to conservation of atomic number,

  $\begin{array}{c}A+91=90\\ A=90-91\\ A=-1\end{array}$

So, the missing element is beta particle.

Similarly, total mass number on right side of the equation is $=M+234$

  $\begin{array}{c}M+234=234\\ M=234-234\\ M=0\end{array}$

So, the balanced nuclear equation: $Th\to Pa+e$