Problem 31 - Chemistry: The Central Science in SI Units, Global Edition

Question

Write the correct symbol, with both superscript and subscript, for each of the following. Use the list of elements in the front inside cover as needed: (a) the isotope of hafnium that contains 106 neutrons, \((\mathbf{b})\) the isotope of mercury with mass number \(201,(\mathbf{c})\) the isotope of rhenium with mass number \(187,(\mathbf{d})\) the isotope of calcium that has an equal number of protons and neutrons.

Step-by-Step Solution

Answer

The correct symbols for the given isotopes are: (a) \(^{178}_{72}Hf\) (b) \(^{201}_{80}Hg\) (c) \(^{187}_{75}Re\) (d) \(^{40}_{20}Ca\)

Step 1: Determine the atomic number of hafnium (Z)

Check the list of elements to find the atomic number (number of protons) of hafnium. Hafnium has an atomic number of 72.

Step 2: Calculate the mass number (A)

Mass number (A) = number of protons (Z) + number of neutrons (N). A = 72 + 106 = 178

Step 3: Write the symbol for the isotope of hafnium

The isotope of hafnium with 106 neutrons is represented as: \(^{178}_{72}Hf\) (b) the isotope of mercury with mass number 201

Step 4: Determine the atomic number of mercury (Z)

Check the list of elements to find the atomic number (number of protons) of mercury. Mercury has an atomic number of 80.

Step 5: Write the symbol for the isotope of mercury

The isotope of mercury with mass number 201 is represented as: \(^{201}_{80}Hg\) (c) the isotope of rhenium with mass number 187

Step 6: Determine the atomic number of rhenium (Z)

Check the list of elements to find the atomic number (number of protons) of rhenium. Rhenium has an atomic number of 75.

Step 7: Write the symbol for the isotope of rhenium

The isotope of rhenium with mass number 187 is represented as: \(^{187}_{75}Re\) (d) the isotope of calcium that has an equal number of protons and neutrons

Step 8: Determine the atomic number of calcium (Z)

Check the list of elements to find the atomic number (number of protons) of calcium. Calcium has an atomic number of 20.

Step 9: Calculate the mass number (A)

Since the isotope of calcium has equal numbers of protons and neutrons, the mass number (A) is double the number of protons. A = 2 * 20 = 40

Step 10: Write the symbol for the isotope of calcium

The isotope of calcium with an equal number of protons and neutrons is represented as: \(^{40}_{20}Ca\)

Key Concepts

Atomic Number

The atomic number is a fundamental characteristic of an element that tells us the number of protons in the nucleus of an atom. It is denoted by the symbol \(Z\). Each element in the periodic table has a unique atomic number, which helps to identify it.
This concept is crucial because the atomic number determines the identity of the element. For example, hydrogen, with one proton, has an atomic number of 1, whereas helium, with two protons, has an atomic number of 2.
Moreover, the atomic number is always equal to the number of protons and, in a neutral atom, also the number of electrons. This balance of protons and electrons means the atom is electrically neutral and stable.
Knowing the atomic number is the first step in identifying isotopes and determining their specific characteristics. For instance, in our exercise:

• Hafnium has \(Z = 72\).
• Mercury has \(Z = 80\).
• Rhenium has \(Z = 75\).
• Calcium has \(Z = 20\).

Mass Number

The mass number is the sum of the number of protons and neutrons in the nucleus of an atom. It is denoted by the symbol \(A\) and provides insight into the isotope of an element. Unlike the atomic number, which is unique for each element, elements can have multiple isotopes, each with a different mass number.
The mass number is not shown in the periodic table because it varies with isotopes. For example, carbon typically has two important isotopes: carbon-12 and carbon-14, where the numbers 12 and 14 are the mass numbers.
To calculate the mass number, add the number of protons (atomic number) to the number of neutrons.
In the exercise, the calculation of the mass number is shown as:

• For hafnium with 106 neutrons: \(A = 72 + 106 = 178\).
• For mercury given a mass number of 201, no additional information was needed.
• For rhenium given a mass number of 187, also direct.
• For calcium with an equal number of protons and neutrons: \(A = 2 \times 20 = 40\).

Elements

Elements are the basic building blocks of matter and are pure substances consisting of only one type of atom. Each element is defined by its atomic number, which corresponds to the number of protons in its nucleus. This sets each element apart from the others.
There are over 100 elements listed in the periodic table, starting from hydrogen to oganesson. Each element has unique properties that define its behavior in reactions and its occurrence in nature.
Elements can exist as single atoms, molecules, or in various combinations in compounds. They are classified into metals, non-metals, and metalloids, each group showcasing distinct physical and chemical properties.
For the purpose of isotopes, a single element such as hafnium, mercury, rhenium, or calcium can exist in multiple forms, each having a different number of neutrons but the same atomic number, thus maintaining the same elemental identity.
Understanding elements is crucial as it helps us navigate from the atomic scale to the complex materials we see around us.