Chapter 2, Problem 2.28P

(a)

Interpretation Introduction

Interpretation:Whether the pair $\text{O}$ and $\text{O}$ has same number of protons,neutrons and electrons or not should be determined. Also whether the pair $\text{O}$ and $\text{O}$ has same value of mass number $\left(\text{A}\right)$ , atomic number $\left(\text{Z}\right)$ and neutron number $\left(\text{N}\right)$ or not should be determined.

Concept introduction:Total number of protons in an element is known as its atomic number and it is represented with symbol $\text{Z}$ . Atom has equal number of protons and electrons to maintain its electrical neutrality. Mass number $\left(\text{A}\right)$ of any isotope of an element is determined by the addition of its atomic number $\left(\text{Z}\right)$ with its neutron number $\left(\text{N}\right)$ .

Formula to relate neutron number $\left(\text{N}\right)$ , mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Explanation of Solution

Nuclide notation of an atom is represented as follows:

  $\text{X}$

Where,

• X is atomic symbol of an element.
• $\text{A}$is the mass number.
• $\text{Z}$is the atomic number (number of protons) of that element.

In $\text{O}\text{and}\text{O}$ have same atomic numbers so they have the same number of protons (8) and electrons (8). Their mass numbers are different $\left(\text{A}\right)$ .

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{O}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{O}$ is 8.

Mass number $\left(\text{A}\right)$ of $\text{O}$ is 16.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =16-8\\ =8\end{array}$

Hence, neutron number $\left(\text{N}\right)$ of $\text{O}$ is $8$ .

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{O}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{O}$ is 8.

Mass number $\left(\text{A}\right)$ of $\text{O}$ is 17.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =17-8\\ =9\end{array}$

Hence, neutron number $\left(\text{N}\right)$ of $\text{O}$ is 9.

So,atomic number of $\text{O}$ and $\text{O}$ are same.

(b)

Interpretation Introduction

Interpretation:Whether the pair $\text{A}\text{r}$ and $\text{K}$ has same number of protons,neutrons and electrons or not should be determined. Also whether the pair $\text{A}\text{r}$ and $\text{K}$ has same value of mass number $\left(\text{A}\right)$ , atomic number $\left(\text{Z}\right)$ and neutron number $\left(\text{N}\right)$ or not should be determined.

Concept introduction:Total number of protons in an element is known as its atomic number and it is represented with symbol $\text{Z}$ . Atom has equal number of protons and electrons to maintain its electrical neutrality. Mass number $\left(\text{A}\right)$ of any isotope of an element is determined by the addition of its atomic number $\left(\text{Z}\right)$ with its neutron number $\left(\text{N}\right)$ .

Formula to relate neutron number $\left(\text{N}\right)$ , mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Explanation of Solution

Nuclide notation of an atom is represented as follows:

  $\text{X}$

Where,

• X is atomic symbol of an element.
• $\text{A}$is the mass number.
• $\text{Z}$is the atomic number (number of protons) of that element.

In $\text{A}\text{r}$ and $\text{K}$ , they have different atomic numbers $\left(\text{Z}\right)$ , so they have different numbers of protons and electrons. Their mass numbers $\left(\text{A}\right)$ are also different.

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{A}\text{r}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{A}\text{r}$ is 18.

Mass number $\left(\text{A}\right)$ of $\text{A}\text{r}$ is 40.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =40-18\\ =22\end{array}$

Hence neutron number $\left(\text{N}\right)$ of $\text{A}\text{r}$ is 22.

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{K}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{K}$ is 19.

Mass number $\left(\text{A}\right)$ of $\text{K}$ is 41.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =41-19\\ =22\end{array}$

Hence neutron number $\left(\text{N}\right)$ of $\text{K}$ is 22.

So, neutron number $\left(\text{N}\right)$ , in $\text{A}\text{r}$ and $\text{K}$ are same.

(c)

Interpretation Introduction

Interpretation:Whether the pair $\text{C}\text{o}$ and $\text{N}\text{i}$ has same number of protons,neutrons and electrons or not should be determined. Also whether the pair $\text{C}\text{o}$ and $\text{N}\text{i}$ has same value of mass number $\left(\text{A}\right)$ , atomic number $\left(\text{Z}\right)$ and neutron number $\left(\text{N}\right)$ or not should be determined.

Concept introduction:Total number of protons in an element is known as its atomic number and it is represented with symbol $\text{Z}$ . Atom has equal number of protons and electrons to maintain its electrical neutrality. Mass number $\left(\text{A}\right)$ of any isotope of an element is determined by the addition of its atomic number $\left(\text{Z}\right)$ with its neutron number $\left(\text{N}\right)$ .

Formula to relate neutron number $\left(\text{N}\right)$ , mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Explanation of Solution

Nuclide symbol of an atom is represented as $\text{X}$ , where X is the atomic symbol of an element, A is the mass number and Z is the atomic number (number of protons) of that element.

  $\text{C}\text{o}$ and $\text{N}\text{i}$ have same mass number as their $\left(\text{A}\right)$ values are same. Their atomic numbers $\left(\text{Z}\right)$ are different so the number of protons and the number of electrons are different.

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{C}\text{o}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{C}\text{o}$ is 27.

Mass number $\left(\text{A}\right)$ of $\text{C}\text{o}$ is60.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =60-27\\ =33\end{array}$

Hence neutron number $\left(\text{N}\right)$ of $\text{C}\text{o}$ is 33.

Formula to calculate the neutron number $\left(\text{N}\right)$ of $\text{N}\text{i}$ , from its mass number $\left(\text{A}\right)$ and atomic number $\left(\text{Z}\right)$ is as follows:

  $\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)$

Atomic number $\left(\text{Z}\right)$ of $\text{N}\text{i}$ is 28.

Mass number $\left(\text{A}\right)$ of $\text{N}\text{i}$ is 60.

Substitute the values in above formula.

  $\begin{array}{c}\text{Neutron number}\left(\text{N}\right)=\text{Mass number}\left(\text{A}\right)-\text{Atomic number}\left(\text{Z}\right)\\ =60-28\\ =32\end{array}$

Hence neutron number $\left(\text{N}\right)$ of $\text{N}\text{i}$ is 32.Somass number in $\text{C}\text{o}$ and $\text{N}\text{i}$ are same.