Chapter 18, Problem 74QRT

(a)

Interpretation Introduction

Interpretation:

Balanced nuclear equation has to be given for the below equation,

    $\text{U}\text{+}\text{N}\stackrel{}{\to }\boxed{}+5\text{n}$

Concept Introduction:

Nuclear reaction is the one where the nucleus of the atom is involved in the reaction.  This can be represented in form of a nuclear equation.  Missing particle in a nuclear equation can be identified by using the mass number and atomic number balance.

Explanation of Solution

Given nuclear equation is,

    $\text{U}\text{+}\text{N}\stackrel{}{\to }\boxed{}+5\text{n}$

The unknown particle can be assigned as $\text{X}$.  Therefore, the given nuclear equation can be rewritten as,

  $\text{U}\text{+}\text{N}\stackrel{}{\to }\text{X}+5\text{n}$

Mass number of the particle formed:

    $\begin{array}{l}\text{238}+\text{14}\text{=}\text{A}+5\\ \text{A}\text{=}\text{252}\text{-}\text{5}\\ \text{A}\text{=}\text{247}\end{array}$

Atomic number of the particle formed:

    $\begin{array}{l}92+7\text{=}\text{Z}\text{+}\text{0}\\ \text{Z}\text{=}99\end{array}$

Therefore, the atomic number of the particle is 99 and mass number is 247.  The particle with atomic number 99 is Einsteinium.  Therefore, the complete balanced nuclear equation can be given as,

    $\text{U}\text{+}\text{N}\stackrel{}{\to }\text{E}\text{s}+5\text{n}$

(b)

Interpretation Introduction

Interpretation:

Balanced nuclear equation has to be given for the below equation,

    $\text{U}\text{+}\boxed{}\stackrel{}{\to }\text{F}\text{m}+5\text{n}$

Concept Introduction:

Refer part (a).

Explanation of Solution

Given nuclear equation is,

    $\text{U}\text{+}\boxed{}\stackrel{}{\to }\text{F}\text{m}+5\text{n}$

The unknown particle can be assigned as $\text{X}$.  Therefore, the given nuclear equation can be rewritten as,

  $\text{U}\text{+}\text{X}\stackrel{}{\to }\text{F}\text{m}+5\text{n}$

Mass number of the particle formed:

    $\begin{array}{l}\text{238}+\text{A}\text{=}\text{249}+5\\ \text{A}\text{=}\text{254}\text{-}\text{238}\\ \text{A}\text{=}\text{16}\end{array}$

Atomic number of the particle formed:

    $\begin{array}{l}92+\text{Z}\text{=}\text{100}\text{+}\text{0}\\ \text{Z}\text{=}8\end{array}$

Therefore, the atomic number of the particle is 8 and mass number is 16.  The particle with atomic number 8 is Oxygen.  Therefore, the complete balanced nuclear equation can be given as,

    $\text{U}\text{+}\text{O}\stackrel{}{\to }\text{F}\text{m}+5\text{n}$

(c)

Interpretation Introduction

Interpretation:

Balanced nuclear equation has to be given for the below equation,

    $\text{E}\text{s}\text{+}\boxed{}\stackrel{}{\to }\text{M}\text{d}+\text{n}$

Concept Introduction:

Refer part (a).

Explanation of Solution

Given nuclear equation is,

    $\text{E}\text{s}\text{+}\boxed{}\stackrel{}{\to }\text{M}\text{d}+\text{n}$

The unknown particle can be assigned as $\text{X}$.  Therefore, the given nuclear equation can be rewritten as,

  $\text{E}\text{s}\text{+}\text{X}\stackrel{}{\to }\text{M}\text{d}+\text{n}$

Mass number of the particle formed:

    $\begin{array}{l}\text{253}+\text{A}\text{=}\text{256}+1\\ \text{A}\text{=}\text{257}\text{-}\text{253}\\ \text{A}\text{=}\text{4}\end{array}$

Atomic number of the particle formed:

    $\begin{array}{l}99+\text{Z}\text{=}\text{101}\text{+}\text{0}\\ \text{Z}\text{=}2\end{array}$

Therefore, the atomic number of the particle is 2 and mass number is 4.  The particle with atomic number 2 is Helium.  Therefore, the complete balanced nuclear equation can be given as,

    $\text{E}\text{s}\text{+}\text{H}\text{e}\stackrel{}{\to }\text{M}\text{d}+\text{n}$

(d)

Interpretation Introduction

Interpretation:

Balanced nuclear equation has to be given for the below equation,

    $\text{C}\text{m}\text{+}\boxed{}\stackrel{}{\to }\text{N}\text{o}+4\text{n}$

Concept Introduction:

Refer part (a).

Explanation of Solution

Given nuclear equation is,

    $\text{C}\text{m}\text{+}\boxed{}\stackrel{}{\to }\text{N}\text{o}+4\text{n}$

The unknown particle can be assigned as $\text{X}$.  Therefore, the given nuclear equation can be rewritten as,

  $\text{C}\text{m}\text{+}\text{X}\stackrel{}{\to }\text{N}\text{o}+4\text{n}$

Mass number of the particle formed:

    $\begin{array}{l}\text{246}+\text{A}\text{=}\text{254}+4\\ \text{A}\text{=}\text{258}\text{-}\text{246}\\ \text{A}\text{=}\text{12}\end{array}$

Atomic number of the particle formed:

    $\begin{array}{l}96+\text{Z}\text{=}\text{102}\text{+}\text{0}\\ \text{Z}\text{=}6\end{array}$

Therefore, the atomic number of the particle is 6 and mass number is 12.  The particle with atomic number 6 is Carbon.  Therefore, the complete balanced nuclear equation can be given as,

    $\text{C}\text{m}\text{+}\text{C}\stackrel{}{\to }\text{N}\text{o}+4\text{n}$

(e)

Interpretation Introduction

Interpretation:

Balanced nuclear equation has to be given for the below equation,

    $\text{C}\text{f}\text{+}\boxed{}\stackrel{}{\to }\text{L}\text{r}+5\text{n}$

Concept Introduction:

Refer part (a).

Explanation of Solution

Given nuclear equation is,

    $\text{C}\text{f}\text{+}\boxed{}\stackrel{}{\to }\text{L}\text{r}+5\text{n}$

The unknown particle can be assigned as $\text{X}$.  Therefore, the given nuclear equation can be rewritten as,

  $\text{C}\text{f}\text{+}\text{X}\stackrel{}{\to }\text{L}\text{r}+5\text{n}$

Mass number of the particle formed:

    $\begin{array}{l}\text{252}+\text{A}\text{=}\text{257}+5\\ \text{A}\text{=}\text{262}\text{-}\text{252}\\ \text{A}\text{=}\text{10}\end{array}$

Atomic number of the particle formed:

    $\begin{array}{l}98+\text{Z}\text{=}\text{103}\text{+}\text{0}\\ \text{Z}\text{=}5\end{array}$

Therefore, the atomic number of the particle is 5 and mass number is 10.  The particle with atomic number 5 is Boron.  Therefore, the complete balanced nuclear equation can be given as,

    $\text{C}\text{f}\text{+}\text{B}\stackrel{}{\to }\text{L}\text{r}+5\text{n}$