Problem 12 - Chemistry and Chemical Reactivity

Question

Give the complete symbol \(\left(\frac{A}{Z} X\right)\) for each of the following atoms: (a) fluorine with 10 neutrons, (b) chromium with 28 neutrons, and (c) xenon with 78 neutrons.

Step-by-Step Solution

Answer

(a) \( \frac{19}{9} F \), (b) \( \frac{52}{24} Cr \), (c) \( \frac{132}{54} Xe \).

Step 1: Understand Atomic Symbols

The notation \( \left(\frac{A}{Z} X\right) \) represents an atomic symbol where \( A \) is the mass number, \( Z \) is the atomic number, and \( X \) is the chemical symbol of the element.

Step 2: Determine the Atomic Number

The atomic number \( Z \) represents the number of protons. For fluorine, \( Z = 9 \). For chromium, \( Z = 24 \). For xenon, \( Z = 54 \). These values are based on the periodic table.

Step 3: Calculate the Mass Number

The mass number \( A \) is the sum of protons and neutrons in an atom. For each atom:(a) Fluorine: \( A = 9 + 10 = 19 \).(b) Chromium: \( A = 24 + 28 = 52 \).(c) Xenon: \( A = 54 + 78 = 132 \).

Step 4: Write the Complete Symbol

Now that we have both \( A \) and \( Z \), we can write the atomic symbols:(a) Fluorine: \( \left(\frac{19}{9} F\right) \).(b) Chromium: \( \left(\frac{52}{24} Cr\right) \).(c) Xenon: \( \left(\frac{132}{54} Xe\right) \).

Key Concepts

Mass Number

The mass number is represented by the letter \( A \) in an atomic symbol. It provides information about the total number of protons and neutrons in an atom's nucleus. The formula to calculate the mass number is: \[ A = Z + ext{Number of Neutrons} \] where \( Z \) is the atomic number. The mass number is crucial because it tells us about the overall size and the isotopic composition of the atom.

• In the case of fluorine, the mass number is calculated as 9 protons plus 10 neutrons, resulting in 19.
• For chromium, it has 24 protons and 28 neutrons, leading to a mass number of 52.
• Xenon includes 54 protons and 78 neutrons, thus making the mass number 132.

Understanding the mass number helps one identify different isotopes of an element, as isotopes differ by the number of neutrons.

Atomic Number

The atomic number, symbolized by \( Z \), represents the number of protons in the nucleus of an atom. It serves as an identifier for chemical elements because each element has a unique atomic number. This number essentially defines the element and determines its position on the periodic table. The atomic number also equals the number of electrons in a neutral atom.

• For example, fluorine has an atomic number of 9, indicating it has 9 protons.
• Chromium has an atomic number of 24, meaning it contains 24 protons.
• Xenon comes with an atomic number of 54, showing it possesses 54 protons.

The atomic number is fundamental to the identity of an element and is used in forming the atomic symbol. Without knowing \( Z \), one cannot accurately identify an element or its chemical properties.

Chemical Elements

Chemical elements are basic building blocks of matter, each defined by its atomic number, which indicates the number of protons in its nucleus. Currently, there are 118 known elements, arranged in the periodic table according to their atomic numbers. Each element is represented by a unique symbol, often derived from its English or Latin name, such as \(F\) for fluorine or \(Xe\) for xenon. Elements can exist in different isotopic forms, which means they have the same number of protons but a different number of neutrons. This variation affects the mass number of the element but not its chemical properties, which are determined by the number of protons and electrons.

• Fluorine, for example, is a reactive nonmetal with atomic number 9 and typically forms compounds like fluoride.
• Chromium is a metallic element found with atomic number 24 and is known for its luster and corrosion resistance.
• Xenon is a noble gas, distinguished by atomic number 54, known for its inertness and application in lighting.

The periodic table serves as a crucial tool to study elements, providing valuable information about each element’s properties and relations to others.