Problem 94 - Chemistry The Central Science In Si Units

Question

The element argon has three naturally occurring isotopes, with \(18,20,\) and 22 neutrons in the nucleus, respectively. (a) Write the full chemical symbols for these three isotopes. (b) Describe the similarities and differences between the three kinds of atoms of argon.

Step-by-Step Solution

Answer

Argon isotopes are \(^{36}_{18}\text{Ar}\), \(^{38}_{18}\text{Ar}\), and \(^{40}_{18}\text{Ar}\). They have the same number of protons but differ in neutron count.

Step 1: Understanding Isotope Symbols

The full chemical symbol for an isotope is written as \(^{A}_{Z}X\), where \(A\) is the mass number, \(Z\) is the atomic number, and \(X\) is the chemical symbol. For argon, the atomic number \(Z\) is 18.

Step 2: Calculating Mass Numbers

The mass number \(A\) for each isotope is calculated as the sum of protons and neutrons. Since argon always has 18 protons (atomic number), the mass numbers for isotopes with 18, 20, and 22 neutrons will be calculated as follows: - \(A = 18 + 18 = 36\)- \(A = 18 + 20 = 38\)- \(A = 18 + 22 = 40\).

Step 3: Writing Isotope Symbols

Using the mass numbers calculated in Step 2, the full chemical symbols for the three isotopes of argon are:1. \(^{36}_{18}\text{Ar}\)2. \(^{38}_{18}\text{Ar}\)3. \(^{40}_{18}\text{Ar}\).

Step 4: Comparing Isotopes

The isotopes of argon have the same number of protons and electrons, making them chemically similar. However, they differ in the number of neutrons. Specifically, they have 18, 20, and 22 neutrons, respectively, which affects their mass and physical properties, such as density and stability.

Key Concepts

Mass Number

The mass number is a fundamental concept in understanding atomic structure. It is symbolized by the letter \(A\). Essentially, the mass number represents the sum of protons and neutrons present in the nucleus of an atom.
This is crucial because it helps differentiate between isotopes of the same element.
When dealing with isotopes, the mass number can vary even though the element has the same atomic number. For argon isotopes, let's break it down:

• For an isotope with 18 neutrons, the mass number is calculated as \(18 \text{ (protons)} + 18 \text{ (neutrons)} = 36\).
• With 20 neutrons, the mass number becomes \(18 + 20 = 38\).
• For 22 neutrons, it is \(18 + 22 = 40\).

Understanding the mass number is essential because it gives insight into the different properties of isotopes, such as the differences in their masses and how these can affect their stability and physical characteristics.

Atomic Number

The atomic number, represented as \(Z\), is a key identifier for elements on the periodic table. It tells us the number of protons present in the nucleus of an atom.
For argon, as specified in the problem, the atomic number is always 18. This is because every atom of argon has 18 protons regardless of its isotope.
The atomic number is of utmost importance because it defines the chemical element itself. When you encounter an atomic number, you can directly identify the element, as each number corresponds uniquely to one specific element.

• An atomic number of 18 is unique to argon, which means any atom with 18 protons is identified as argon.
• This property remains unchanged across various isotopes of argon.

Thus, the atomic number is crucial for understanding the basic identity of the element, keeping the chemical properties consistent across isotopes.

Chemical Symbol

The chemical symbol is a concise representation of an element, typically one or two letters long. For argon, the chemical symbol is \(\text{Ar}\). This notation is standardized in the scientific community for easy reference.
The chemical symbol serves as a key part of the isotope notation, which combines the mass number, atomic number, and chemical symbol to represent specific forms of atoms. For example, the isotopes of argon mentioned are written as:

• \(^{36}_{18}\text{Ar}\)
• \(^{38}_{18}\text{Ar}\)
• \(^{40}_{18}\text{Ar}\)

Each of these symbols shows at a glance not only the element but also the specific isotope it represents.
It is an essential shorthand used to convey a lot of information about the atomic composition and identity quickly and clearly, facilitating communication and understanding in the world of chemistry.