Chapter 2, Problem 105AP

Interpretation Introduction

Interpretation:

The number of protons, neutrons, and the ratio of neutrons to protons for each of the noble gas areto be determined. Any general trend discovered in this changes is to be described.

Concept introduction:

The atomic number $(Z)$ is the number of protons in the nucleus of each atom of an element. It also indicates the number of electrons in an atom. Mathematically, it can be represented as follows:

$\text{Atomic number}(Z)=\text{ No}\text{. of electrons or protons}$

Mass number $(A)$ is the total number of protons and neutrons present in the nucleus of an atom of an element. Mathematically, it can be represented as follows:

$\text{Mass number}(A)=\text{ No}\text{. of protons (Z) + No}\text{. of neutrons}$

The atomic number together with themass number of the element with symbol X is represented by the expression as follows:

${}_{\text{Z}}^{\text{A}}\text{X}$

Here, A is the mass number $\left(\text{number of protons + number of neutrons}\right)$, Z is the atomic number $\left(\text{number of protons}\right)$, and X is the symbol of an element.

The number of neutrons is calculated by the relation:

$\text{A}-\text{Z}$

Here, A is mass number and Z is atomic number.

Answer to Problem 105AP

Solution:

For ${}_{{}_2}^4\text{He}-\text{2 p, 2 n}$, for ${}_{{}_{10}}^{20}\text{Ne}-10\text{ p, 10n}$, for ${}_{{}_{18}}^{40}\text{Ar}-18\text{ p, 22n}$, for ${}_{36}^{84}\text{Kr}-36\text{p},48\text{n}$, and for ${}_{54}^{132}\text{Xe}-54\text{ p, 78n}$.

The neutrons to protons ratio of ${}_{{}_2}^4\text{He},{}_{{}_{10}}^{20}\text{Ne},{}_{{}_{18}}^{40}\text{Ar},{}_{36}^{84}{\text{Kr, and }}_{54}^{132}\text{Xe}$ are $1.00,1.00,1.22,1.33,\text{and }1.44$, respectively.

Explanation of Solution

(a) The number of protons and neutrons in the nucleus of each atom

The atomic number and mass number of the element X are represented as follows:

${}_{\text{Z}}^{\text{A}}\text{X}$

Here, A is the mass number $\left(\text{number of protons}+\text{number of neutrons}\right)$, Z is the atomic number $\left(\text{number of protons}\right)$, and X is the symbol of an element.

The number of protons and neutrons in ${}_{{}_2}^4\text{He}$ is as follows:

The number of protons is equal to the atomic number $\text{Z}$.

The atomic number is $2$, so there are $2$ protons.

The number of neutrons $=\text{A}-\text{Z}$.

The mass number is $4$, so the number of neutrons is $4-2=2$.

The number of protons and neutrons in ${}_{{}_{10}}^{20}\text{Ne}$ is as follows:

The number of protons is equal to the atomic number $\text{Z}$.

The atomic number is $10$, so there are $10$ protons.

The number of neutrons $=\text{A}-\text{Z}$.

The mass number is $20$, so the number of neutrons is $20-10=10$.

The number of protons and neutrons in ${}_{{}_{18}}^{40}\text{Ar}$ is as follows:

The number of protons is equal to the atomic number $\text{Z}$.

The atomic number is $18$, so there are $18$ protons.

The number of neutrons $=\text{A}-\text{Z}$.

The mass number is $40$, so the number of neutrons is $40-18=22$.

The number of protons and neutrons in ${}_{36}^{84}\text{Kr}$ is as follows:

The number of protons is equal to the atomic number $\text{Z}$.

The atomic number is $36$, so there are $36$ protons.

The number of neutrons $=\text{A}-\text{Z}$.

The mass number is $84$, so the number of neutrons is $84-36=48$.

The number of protons and neutrons in ${}_{54}^{132}\text{Xe}$ is as follows:

The number of protons is equal to the atomic number $\text{Z}$.

The atomic number is $54$, so there are $54$ protons.

The number of neutrons $=\text{A}-\text{Z}$.

The mass number is $132$, so the number of neutrons is $132-54=78$.

b) The ration of neutrons to protons in the nucleus of each atom

1. The ratio of neutrons to protons in ${}_{{}_2}^4\text{He}$ is as follows:

The number of protons is $2$ and a number of neutrons is $2$.

$\begin{array}{c}\text{Ratio}=\frac{\text{Number}\text{of neutrons}}{\text{Number}\text{of}\text{protons}}\\ =\frac{2}{2}\\ =1.00\end{array}$

2. The ratio of neutrons to protons in ${}_{{}_{10}}^{20}\text{Ne}$ is as follows:

The number of protons is $10$ and a number of neutrons is $10$.

3. The ratio of neutrons to protons in ${}_{{}_{18}}^{40}\text{Ar}$ is as follows:

The number of protons is $18$ and a number of neutrons is $22$.

$\begin{array}{c}\text{Ratio}=\frac{\text{Number}\text{of neutrons}}{\text{Number}\text{of}\text{protons}}\\ =\frac{22}{18}\\ =1.22\end{array}$

4. The ratio of neutrons to protons in ${}_{36}^{84}\text{Kr}$ is as follows:

The number of protons is $36$ and a number of neutrons is $48$.

$\begin{array}{c}\text{Ratio}=\frac{\text{Number}\text{of neutrons}}{\text{Number}\text{of}\text{protons}}\\ =\frac{48}{36}\\ =1.33\end{array}$

5. The ratio of neutrons to protons in ${}_{54}^{132}\text{Xe}$ is as follows:

The number of protons is $54$ and a number of neutrons is $78$.

$\begin{array}{c}\text{Ratio}=\frac{\text{Number}\text{of neutrons}}{\text{Number}\text{of}\text{protons}}\\ =\frac{78}{54}\\ =1.44\end{array}$

The general trend concluded from the neutrons to protons ratio is that the as the atomic number Z increases, the ratio of neutrons to protons also increases.