Chapter 2, Problem 2.22QP

The following radioactive isotopes are used in medicine for things such as imaging organs, studying blood circulation, and treating cancer. Give the number of neutrons present in each isotope: ¹⁹⁸Au, ⁴⁷Ca, ⁶⁰Co, ¹⁸F, ¹²⁵I, ¹³¹I, ⁴²K, ⁴³K, ²⁴Na, ³²P, ⁸⁵Sr, ⁹⁹Tc.

Interpretation Introduction

Interpretation:

The total number of neutrons present in the given set of radioactive isotopes needs to be given.

Concept introduction:

The total number of protons in an atom is said to be its atomic number.  By using the total number of protons and neutrons all the atoms can be identified.  Atomic number is denoted by “Z”.  Atomic number is a characteristic of each and every atom in an element.

The total number of neutrons and protons of an atom is said to be its mass number.  By using the total number of protons and neutrons all the atoms can be identified.  Mass number is denoted by “A”.

Atomic number does not change for atoms present in an element while mass number can change due to difference in number of neutrons.  These are known as isotopes.

Total number of neutrons present in an atom can be found out of finding the difference between mass number and atomic number.

$\text{mass number (A) = number of protons (Z) + number of neutrons}$

To Determine: The number of neutrons present in the given radioactive isotopes.

Answer to Problem 2.22QP

The number of neutrons in ${}^{\text{198}}\text{Au}$ is 119

The number of neutrons in ${}^{\text{47}}\text{Ca}$ is 27

The number of neutrons in ${}^{\text{60}}\text{Co}$ is 33

The number of neutrons in ${}^{\text{18}}\text{F}$ is 9

The number of neutrons in ${}^{\text{125}}\text{I}$ is 72

The number of neutrons in ${}^{\text{131}}\text{I}$ is 78

The number of neutrons in ${}^{\text{42}}\text{K}$ is 23

The number of neutrons in ${}^{\text{43}}\text{K}$ is 24

The number of neutrons in ${}^{\text{24}}\text{Na}$ is 13

The number of neutrons in ${}^{\text{32}}\text{P}$ is 17

The number of neutrons in ${}^{\text{85}}\text{Sr}$ is 47

The number of neutrons in ${}^{\text{99}}\text{Tc}$ is 56

Explanation of Solution

To determine the number of neutrons present in ${}^{\text{198}}\text{Au}$

Atom of the element given= gold

Mass number (A)= 198

Total number of protons (Z)=79

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}198\text{ - 79}\\ =119\end{array}$

Therefore, the mass number of ${}^{\text{198}}\text{Au}$ is 119.

To determine the number of neutrons present in ${}^{\text{47}}\text{Ca}$

Atom of the element given= calcium

Mass number (A)= 47

Total number of protons (Z)=20

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}47\text{ - 20}\\ =27\end{array}$

Therefore, the mass number of ${}^{\text{47}}\text{Ca}$ is 27.

To determine the number of neutrons present in ${}^{\text{60}}\text{Co}$

Atom of the element given= cobalt

Mass number (A)= 60

Total number of protons (Z)=27

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}60\text{ - 27}\\ =33\end{array}$

Therefore, the mass number of ${}^{\text{60}}\text{Co}$ is 33.

To determine the number of neutrons present in ${}^{\text{18}}\text{F}$

Atom of the element given= fluorine

Mass number (A)= 18

Total number of protons (Z)=9

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}18\text{ - 9}\\ =9\end{array}$

Therefore, the mass number of ${}^{\text{18}}\text{F}$ is 9.

To determine the number of neutrons present in ${}^{\text{125}}\text{I}$

Atom of the element given= iodine

Mass number (A)= 125

Total number of protons (Z)=53

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}125\text{ - 53}\\ =72\end{array}$

Therefore, the mass number of ${}^{\text{125}}\text{I}$ is 72.

To determine the number of neutrons present in ${}^{\text{131}}\text{I}$

Atom of the element given= iodine

Mass number (A)= 131

Total number of protons (Z)=53

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}131\text{ - 53}\\ =78\end{array}$

Therefore, the mass number of ${}^{\text{131}}\text{I}$ is 78.

To determine the number of neutrons present in ${}^{\text{42}}\text{K}$

Atom of the element given= potassium

Mass number (A)= 42

Total number of protons (Z)=19

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}42\text{ - 19}\\ =23\end{array}$

Therefore, the mass number of ${}^{\text{42}}\text{K}$ is 23.

To determine the number of neutrons present in ${}^{\text{43}}\text{K}$

Atom of the element given= potassium

Mass number (A)= 43

Total number of protons (Z)=19

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}43\text{ - 19}\\ =24\end{array}$

Therefore, the mass number of ${}^{\text{43}}\text{K}$ is 24.

To determine the number of neutrons present in ${}^{\text{24}}\text{Na}$

Atom of the element given= sodium

Mass number (A)= 24

Total number of protons (Z)=11

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}24\text{ - 11}\\ =13\end{array}$

Therefore, the mass number of ${}^{\text{24}}\text{Na}$ is 13.

To determine the number of neutrons present in ${}^{\text{32}}\text{P}$

Atom of the element given= phosphorous

Mass number (A)= 32

Total number of protons (Z)=15

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}32\text{ - 15}\\ =17\end{array}$

Therefore, the mass number of ${}^{\text{32}}\text{P}$ is 17.

To determine the number of neutrons present in ${}^{\text{85}}\text{Sr}$

Atom of the element given= strontium

Mass number (A)= 85

Total number of protons (Z)=38

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}85\text{ - 38}\\ =47\end{array}$

Therefore, the mass number of ${}^{\text{85}}\text{Sr}$ is 47.

To determine the number of neutrons present in ${}^{\text{99}}\text{Tc}$

Atom of the element given= technitium

Mass number (A)= 99

Total number of protons (Z)=43

The number of neutrons in any atom can be got by finding the difference between mass number and total number of protons.

$\begin{array}{l}\text{Mass number (A) = Total number of protons (Z) + Total number of neutrons}\\ \text{Total number of neutrons}\text{= Mass number (A) - Total number of protons (Z)}\\ \text{=}99\text{ - 43}\\ =56\end{array}$

Therefore, the mass number of ${}^{\text{99}}\text{Tc}$ is 56.

Conclusion

The number of neutrons in the given set of radioisotopes was determined.