Chapter 19, Problem 55A

Interpretation Introduction

Interpretation: The number of protons and neutrons should be calculated in isotopic forms of aluminum, ${}_{\text{13}}^{\text{27}}{\text{Al, }}_{\text{13}}^{\text{28}}{\text{Al and }}_{\text{13}}^{\text{29}}\text{Al}$ .

Concept Introduction: The general atomic symbol of an element is:

  ${}_{\text{Z}}^{\text{A}}\text{X}$

Where A is mass number of an atom, Z is atomic number, and X is the atomic symbol of an element.

Answer to Problem 55A

For ${}_{\text{13}}^{\text{27}}\text{Al}$ :

  $\begin{array}{l}\text{Number of protons = 13}\\ \text{Number of neutrons = 14}\end{array}$

For ${}_{\text{13}}^{\text{28}}\text{Al}$ :

  $\begin{array}{l}\text{Number of protons = 13}\\ \text{Number of neutrons = 15}\end{array}$

For ${}_{\text{13}}^{\text{29}}\text{Al}$ :

  $\begin{array}{l}\text{Number of protons = 13}\\ \text{Number of neutrons = 16}\end{array}$

Explanation of Solution

The number of protons of an atom is equal to the atomic number of an atom. For a neutral atom, the number of protons and electrons are same whereas the mass number of an atom is total sum of number of protons and neutrons of an atom.

Since,

Atomic number = Number of protons

Mass number = Number of neutrons + number of protons

So, from the symbols of given isotope:

 - ${}_{\text{13}}^{\text{27}}\text{Al}$:

The mass number = 27 and atomic number = 13

Using, atomic number = Number of protons:

The number of protons of given isotope = 13.

Using, Mass number = Number of neutrons + number of protons, the number of neutrons present in the isotope can be determined as:

  $\begin{array}{l}\text{27 = Number of neutrons + 13}\hfill \\ \text{Number of neutrons = 27 – 13}\hfill \\ \text{Number of neutrons = 14}\hfill \end{array}$

 - ${}_{\text{13}}^{\text{28}}\text{Al}$:

The mass number = 28 and atomic number = 13

Using, atomic number = Number of protons:

The number of protons of given isotope = 13.

Using, Mass number = Number of neutrons + number of protons, the number of neutrons present in the isotope can be determined as:

  $\begin{array}{l}\text{28 = Number of neutrons + 13}\hfill \\ \text{Number of neutrons = 28 – 13}\hfill \\ \text{Number of neutrons = 15}\hfill \end{array}$

 - ${}_{\text{13}}^{\text{29}}\text{Al}$:

The mass number = 29 and atomic number = 13

Using, atomic number = Number of protons:

The number of protons of given isotope = 13.

Using, Mass number = Number of neutrons + number of protons, the number of neutrons present in the isotope can be determined as:

  $\begin{array}{l}\text{29 = Number of neutrons + 13}\hfill \\ \text{Number of neutrons = 29 – 13}\hfill \\ \text{Number of neutrons = 16}\hfill \end{array}$