Chapter 8, Problem 12PEB

(a)

To determine

The number of protons, neutrons and electrons in an isotope $\text{C}$.

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{C}$ are 6, 6, and 6 respectively.

Explanation of Solution

Given data:

The symbol of an isotope is $\text{C}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is, $\text{X}$.

Compare the standard representation of an element with the symbol of an given isotope that is $\text{C}$ and find the mass and atomic number.

$\text{A}=\text{12}$ and $\text{Z}=6$

Use the formula of mass number and rearrange it for the number of neutrons.

$\text{N}=\text{A}-\text{Z}$,

Substitute $6$ for $\text{Z}$ and $\text{12}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =12-6\\ =6\end{array}$

Since, the number of electrons is exactly equal to the number of protons for every atom. Hence, number of protons = 6, neutrons = 6 and electrons = 6.

Conclusion:

The number of protons, neutrons and electrons in an isotope $\text{C}$ is are 6, 6, and 6 respectively.

(b)

To determine

The number of protons, neutrons and electrons in an isotope $\text{H}$.

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{H}$ are 1, 0 and 1 respectively.

Explanation of Solution

Given data:

The isotope $\text{H}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is, $\text{X}$.

Compare the standard representation of an element with the symbol of the given isotope that is $\text{X}$ and find the mass and atomic number.

$\text{A}=\text{1}$ and $\text{Z}=1$

Use the formula of mass number and rearrange it for the number of neutrons.

$\text{N}=\text{A}-\text{Z}$,

Substitute $1$ for $\text{Z}$ and $\text{1}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =1-1\\ =0\end{array}$

Since, the number of electrons are exactly equal to the number of protons for every atom. Hence, number of protons = 1, neutrons = 0 and electrons = 1.

Conclusion:

Hence, the number of protons, neutrons and electrons in an isotope $\text{H}$ are 1, 0, and 1.

(c)

To determine

The number of protons, neutrons and electrons in an isotope of $\text{A}\text{r}$.

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{A}\text{r}$ are 18, 22, and 18 respectively.

Explanation of Solution

Given data:

The isotope $\text{A}\text{r}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is $\text{X}$.

Compare the standard representation of an element with the symbol of the given isotope that is $\text{A}\text{r}$ and find the mass and atomic number.

$\text{A}=40$ and $\text{Z}=18$

Use the formula of mass number and rearrange it for the number of neutrons.

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

Substitute $18$ for $\text{Z}$ and $\text{40}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =40-18\\ =22\end{array}$

Since, the number of electrons are exactly equal to the number of protons for every atom. Hence, number of protons = 18, neutrons = 22, and electrons = 18.

Conclusion:

Hence, the number of protons, neutrons and electrons in an isotope $\text{A}\text{r}$ are,

18, 22, and 18 respectively.

(d)

To determine

The number of protons, neutrons and electrons in an isotope $\text{H}$

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{H}$ are 1, 1 and 1 respectively.

Explanation of Solution

Given data:

The isotope $\text{H}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is $\text{X}$.

Compare the standard representation of an element with the symbol of the given isotope that is $\text{H}$ and find the mass and atomic number.

$\text{A}=2$ and $\text{Z}=1$

Use the formula of mass number and rearrange it for the number of neutrons.

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

Substitute $1$ for $\text{Z}$ and $\text{2}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =2-1\\ =1\end{array}$

Since, the number of electrons is exactly equal to the number of protons for every atom. Hence, number of protons = 1, neutrons = 1, electrons = 1

Conclusion:

Hence, the number of protons, neutrons and electrons in an isotope $\text{H}$ are 1, 1, and 1 respectively.

(e)

To determine

The number of protons, neutrons and electrons in an isotope $\text{A}\text{u}$.

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{A}\text{u}$ are 79, 118 and 79 respectively.

Explanation of Solution

Given data:

The isotope $\text{A}\text{u}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is $\text{X}$.

Compare the standard representation of an element with the symbol of the given isotope that is $\text{A}\text{u}$ and find the mass and atomic number.

$\text{A}=\text{197}$ and $\text{Z}=79$

Use the formula of mass number and rearrange it for the number of neutrons.

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

Substitute $79$ for $\text{Z}$ and $\text{197}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =197-79\\ =118\end{array}$

Since, the number of electrons is exactly equal to the number of protons for every atom. Hence, number of protons = 79, neutrons = 118 and electrons = 79.

Conclusion:

Hence, the number of protons, neutrons and electrons in an isotope $\text{A}\text{u}$ are 79, 118 and 79 respectively.

(f)

To determine

The number of protons, neutrons and electrons in an isotope $\text{U}$.

Answer to Problem 12PEB

Solution:

The number of protons, neutrons and electrons in an isotope $\text{U}$ are 92, 143 and 92 respectively.

Explanation of Solution

Given data:

The isotope $\text{U}$.

Formula used:

The formula for mass number is as follows;

$\text{A}=\text{N}+\text{Z}$

Here A is the mass number, N is the neutron number and Z is the proton number.

Explanation:

For an element say X the representation of mass number A and atomic mass Z is $\text{X}$.

Compare the standard representation of an element with the symbol of the given isotope that is $\text{U}$ and find the mass and atomic number.

$\text{A}=235$ and $\text{Z}=92$

Use the formula of mass number and rearrange it for the number of neutrons.

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

Substitute $95$ for $\text{Z}$ and $\text{235}$ for $\text{A}$.

$\begin{array}{c}\text{N}=\text{A}-\text{Z}\\ =235-95\\ =143\end{array}$

Since, the number of electrons is exactly equal to the number of protons for every atom. Hence, number of protons = 92, neutrons = 143 and electrons = 92.

Conclusion:

Hence, the number of protons, neutrons and electrons in an isotope $\text{U}$ are 92, 143, and 92 respectively.