Question

38\. Write the atomic symbol \(\left(\begin{array}{c}A \\ Z\end{array} \mathrm{X}\right)\) for each of the isotopes described below. a. \(Z=26, A=54\) b. the isotope of iron with 30 neutrons c. number of protons \(=26\), number of neutrons \(=31\) d. the isotope of nitrogen with 7 neutrons e. \(Z=7, A=15\) f. atomic number \(7,\) number of neutrons \(=8\)

Short answer

a. \(\left(\begin{array}{c}54 \\ 26\end{array} \mathrm{Fe}\right)\) b. \(\left(\begin{array}{c}56 \\ 26\end{array} \mathrm{Fe}\right)\) c. \(\left(\begin{array}{c}57 \\ 26\end{array} \mathrm{Fe}\right)\) d. \(\left(\begin{array}{c}14 \\ 7\end{array} \mathrm{N}\right)\) e. \(\left(\begin{array}{c}15 \\ 7\end{array} \mathrm{N}\right)\) f. \(\left(\begin{array}{c}15 \\ 7\end{array} \mathrm{N}\right)\)

Step-by-step solution

a. Z=26, A=54

Given the values of Z and A, we can identify the element from the periodic table. The element with Z=26 is Iron (Fe). So the atomic symbol is: \(\left(\begin{array}{c}54 \\ 26\end{array} \mathrm{Fe}\right)\) b.

b. the isotope of iron with 30 neutrons

Iron has the atomic number Z=26. To find the mass number, we add the number of protons (Z) and neutrons together: A = Z + neutrons = 26 + 30 = 56 Thus, the atomic symbol is: \(\left(\begin{array}{c}56 \\ 26\end{array} \mathrm{Fe}\right)\) c.

c. number of protons = 26, number of neutrons = 31

In this case, we can find the atomic symbol of the element with Z=26, which is Iron (Fe). Then, we find the mass number by adding the protons and neutrons: A = 26 + 31 = 57 Thus, the atomic symbol is: \(\left(\begin{array}{c}57 \\ 26\end{array} \mathrm{Fe}\right)\) d.

d. the isotope of nitrogen with 7 neutrons

Nitrogen has an atomic number (Z) of 7. We can find the mass number (A) by adding the number of protons (7) and neutrons (7): A = 7 + 7 = 14 Thus, the atomic symbol is: \(\left(\begin{array}{c}14 \\ 7\end{array} \mathrm{N}\right)\) e.

e. Z=7, A=15

Given the values of Z and A, we can identify the element from the periodic table. The element with Z=7 is Nitrogen (N). So the atomic symbol is: \(\left(\begin{array}{c}15 \\ 7\end{array} \mathrm{N}\right)\) f.

f. atomic number 7, number of neutrons =8

The element with the atomic number 7 is Nitrogen (N). To find the mass number, we add the number of protons (Z) and neutrons together: A = Z + neutrons = 7 + 8 = 15 Thus, the atomic symbol is: \(\left(\begin{array}{c}15 \\ 7\end{array} \mathrm{N}\right)\)

Key concepts

Atomic Number

The atomic number, denoted by the symbol \( Z \), is one of the most fundamental properties of an element. It represents the number of protons found in the nucleus of an atom. Since protons carry a positive charge, the atomic number also determines the number of electrons surrounding the nucleus, provided the atom is neutral.
For example, in the exercise provided, iron has an atomic number \( Z = 26 \). This means every iron atom contains 26 protons and, in a neutral state, 26 electrons.
Identifying an element by its atomic number is crucial because it distinguishes one element from another uniquely.

• Each element in the periodic table is arranged in order of increasing atomic number.
• The atomic number directly influences the chemical properties of the element.
• Isotopes of an element have the same atomic number but different mass numbers due to varying neutron counts.

Mass Number

The mass number, symbolized as \( A \), is the total count of protons and neutrons in an atom's nucleus. Unlike the atomic number, which is unique to each element, the mass number can vary within atoms of the same element, leading to the formation of isotopes.
Calculating the mass number is straightforward:

• Mass number \( A = \) number of protons \( + \) number of neutrons.
• The mass number indicates the total mass of the atom's nucleus, as protons and neutrons each contribute approximately 1 atomic mass unit.

In the example from the exercise, for instance, an isotope of iron is described as having 31 neutrons. Since iron has 26 protons, the mass number would be \( A = 26 + 31 = 57 \).
This process shows how the mass number can help to identify specific isotopes of an element.

Periodic Table

The periodic table is an organized tabular display of chemical elements, arranged by increasing atomic number. Each element is positioned based on its atomic number, electron configuration, and recurring chemical properties. This arrangement helps scientists and students to understand elemental relationships, behaviors, and properties.
The periodic table's structure includes horizontal rows called periods and vertical columns known as groups or families.

• Elements within the same group exhibit similar chemical properties.
• Atomic numbers increase from left to right across a period.
• The periodic table provides a framework for evaluating molecular behavior and atomic composition of compounds.

In dealing with isotopes, the periodic table remains a valuable tool. By knowing the atomic number (like \( Z = 7 \) for nitrogen), one can quickly identify an element and then explore its various isotopes by considering differences in their mass numbers.