Chapter 2, Problem 2.16QP

Indicate the number of protons, neutrons, and electrons in each of the following species:

$\text{N}\text{, }\text{S}\text{, }\text{C}\text{u, }\text{S}\text{r, }\text{B}\text{a, }\text{W}\text{, }\text{H}\text{g}$

Interpretation Introduction

Interpretation:

The number of protons, neutrons and electrons in given species has to be identified.

Concept Introduction:

Mass number(A): Mass number of an element is sum of protons and neutrons of the atom.

$\text{A= Number of protons}\left(\text{P}\right)\text{ + Number of neutrons}\left(\text{n}\right)$

Consider an element X with atomic number and mass number,

${}_Z^A\text{X}$

Where,

A is mass number and Z is atomic number ( number of proton or electron)

Answer to Problem 2.16QP

Number of proton, neutron and electrons for given species are given as follows.

Isotopes	${}_{\text{7}}^{\text{15}}\text{N}$	${}_{\text{16}}^{\text{33}}\text{S}$	${}_{\text{29}}^{\text{63}}\text{Cu}$	${}_{\text{38}}^{\text{84}}\text{Sr}$	${}_{\text{56}}^{\text{130}}\text{Ba}$	${}_{\text{74}}^{\text{186}}\text{W}$	${}_{\text{80}}^{\text{202}}\text{Hg}$
No. of Protons	7	16	29	38	56	74	80
No. of Neutrons	8	17	34	46	74	112	122
No. of Electrons	7	16	29	38	56	74	80

Explanation of Solution

For ${}_{\text{7}}^{\text{15}}\text{N}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X =}}_{\text{7}}^{\text{15}}\text{N}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 7}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 15 = 7 + n}\\ \text{n}\text{=8}\end{array}$

For ${}_{\text{16}}^{\text{33}}\text{S}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X =}}_{\text{16}}^{\text{33}}\text{S}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 16}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 33 = 16 + n }\\ \text{n}\text{=17}\end{array}$

For ${}_{\text{29}}^{\text{63}}\text{Cu}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X = }}_{\text{29}}^{\text{63}}\text{Cu}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 29}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 63 = 29 + n }\\ \text{n}\text{=34}\end{array}$

For ${}_{\text{38}}^{\text{84}}\text{Sr}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X = }}_{\text{38}}^{\text{84}}\text{Sr}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 38}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 84 = 38 + n }\\ \text{n}\text{= 46}\end{array}$

For ${}_{\text{56}}^{\text{130}}\text{Ba}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X =}}_{\text{56}}^{\text{130}}\text{Ba}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 56}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 130 = 56 + n }\\ \text{n}\text{=74}\end{array}$

For ${}_{\text{74}}^{\text{186}}\text{W}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X =}}_{\text{74}}^{\text{186}}\text{W}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 74}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 186 = 74 + n }\\ \text{n}\text{= 112}\end{array}$

Thus, the number of neutrons, protons and electrons are found as $44$, $35$ and $35$ respectively.

For ${}_{\text{80}}^{\text{202}}\text{Hg}$, the number of protons, neutrons, and electrons is calculated as follows,

  $\begin{array}{c}{}_{\text{Z}}^{\text{A}}{\text{X = }}_{\text{80}}^{\text{202}}\text{Hg}\\ \text{Z (atomic number) = Number of protons}\\ \text{= 80}\\ \text{A (mass number) = Number of protons (P) + Number of neutrons (N)}\\ \text{ 202 = 80 + n }\\ \text{n}\text{= 122}\end{array}$

Thus, the number of neutrons, protons and electrons are found as $117$, $78$ and $78$ respectively.

Conclusion

The number of protons, neutrons and electrons in given species were identified.