Chapter 2, Problem 2.89QP

(a)

Interpretation Introduction

Interpretation:

The number of protons and neutrons that are present in the given nucleus of noble gases has to be determined.

Answer to Problem 2.89QP

The total number of protons and neutrons present is:

  $\begin{array}{l}{\text{Isotope }}_2^4{\text{He }}_{10}^{20}{\text{Ne }}_{18}^{40}{\text{Ar }}_{36}^{84}{\text{Kr }}_{54}^{132}\text{Xe}\\ \text{No}\text{.of Protons 2 10 18 36 54}\\ \text{No}\text{.of Neutrons 2 10 22 48 78}\end{array}$

Explanation of Solution

Element symbol is given as ${}_{\text{Z}}^{\text{A}}\text{X}$.  Here, A represent the mass number and Z represent the atomic number.

Element symbol given is ${}_2^4\text{He}$:

From the given symbol, it is found that the mass number is 4 and atomic number is 2.  This means the total number of protons present is 2.  Number of neutrons present in the nucleus can be calculated by finding the difference between mass number and atomic number.

In the helium atom, the atomic number 2 is equal to protons number and the differences between the mass number and proton number gives the neutron number 2.

Element symbol given is ${}_{10}^{20}\text{Ne}$:

From the given symbol, it is found that the mass number is 20 and atomic number is 10.  This means the total number of protons present is 10.  Number of neutrons present in the nucleus can be calculated by finding the difference between mass number and atomic number.

In the neon atom, the atomic number 10 is equal to protons number and the differences between the mass number and proton number gives the number of neutrons as 10.

Element symbol given is ${}_{18}^{40}\text{Ar}$:

From the given symbol, it is found that the mass number is 40 and atomic number is 18.  This means the total number of protons present is 18.  Number of neutrons present in the nucleus can be calculated by finding the difference between mass number and atomic number.

In the argon atom, the atomic number 18 is equal to protons number and the differences between the mass number and proton number gives the number of neutrons as 22.

Element symbol given is ${}_{36}^{84}\text{Kr}$:

From the given symbol, it is found that the mass number is 84 and atomic number is 36.  This means the total number of protons present is 36.  Number of neutrons present in the nucleus can be calculated by finding the difference between mass number and atomic number.

In the krypton atom, the atomic number 36 is equal to protons number and the differences between the mass number and proton number gives the number of neutrons as 48.

Element symbol given is ${}_{54}^{132}\text{Xe}$:

From the given symbol, it is found that the mass number is 132 and atomic number is 54.  This means the total number of protons present is 54.  Number of neutrons present in the nucleus can be calculated by finding the difference between mass number and atomic number.

In the xenon atom, the atomic number 54 is equal to protons number and the differences between the mass number and proton number gives the number of neutrons as 78.

Conclusion

Number of protons and neutrons present in the given noble gases are determined.

(b)

Interpretation Introduction

Interpretation:

The ratio of neutrons to protons along with their respective numbers in the nucleus of each atom to be identified.

Answer to Problem 2.89QP

Neutron to proton ratio for noble gases is:

$\begin{array}{l}{\text{Isotope }}_2^4{\text{He }}_{10}^{20}{\text{Ne }}_{18}^{40}{\text{Ar }}_{36}^{84}{\text{Kr }}_{54}^{132}\text{Xe}\\ \text{neutron/proton ratio 1 1 1}\text{.22 1}\text{.33 1}\text{.44}\end{array}$

As the atomic number increases, the neutron to proton ratio also increases.

Explanation of Solution

Analyze the ratio of neutrons to protons for each element.

  $\begin{array}{l}{\text{Isotope }}_2^4{\text{He }}_{10}^{20}{\text{Ne }}_{18}^{40}{\text{Ar }}_{36}^{84}{\text{Kr }}_{54}^{132}\text{Xe}\\ \text{No}\text{.of Protons 2 10 18 36 54}\\ \text{No}\text{.of Neutrons 2 10 22 48 78}\\ \text{Neutron/proton ratio}2/2\text{ 10/10 22/18 48/36 78/54 }\\ \text{ 1}\text{.00 1}\text{.00 1}\text{.22 1}\text{.33 1}\text{.44 }\end{array}$

The ratio of neutron to proton is increasing down the group along with increasing the atomic number.