Problem 14 - Chemistry and Chemical Reactivity

Question

Which of the following are isotopes of element X, the atomic number for which is \(_{9}^{19}\mathrm{g} \mathrm{X},_{9}^{20} \mathrm{g} \mathrm{X},_{18}^{9} \mathrm{X},\) and \(_{9}^{21}\mathrm{g} ?\)

Step-by-Step Solution

Answer

The isotopes of element X are \( _{9}^{19}\mathrm{g} \mathrm{X}, _{9}^{20}\mathrm{g} \mathrm{X}, \) and \( _{9}^{21}\mathrm{g} \).

Step 1: Understand Isotopes

Isotopes are variants of the same chemical element that have the same number of protons but different numbers of neutrons. This means they have the same atomic number but different mass numbers.

Step 2: Identify Atomic Numbers

An element's atomic number is given by the subscript. In this exercise, we are looking for isotopes of element X with atomic number 9.

Step 3: Match with Given Isotopes

Compare each option with atomic number 9:- \( _{9}^{19}\mathrm{g} \mathrm{X} \) has atomic number 9.- \( _{9}^{20}\mathrm{g} \mathrm{X} \) has atomic number 9.- \( _{18}^{9} \mathrm{X} \) has atomic number 18.- \( _{9}^{21}\mathrm{g} \) has atomic number 9.

Step 4: Determine Possible Isotopes

Only the options \( _{9}^{19}\mathrm{g} \mathrm{X} \), \( _{9}^{20}\mathrm{g} \mathrm{X} \), and \( _{9}^{21}\mathrm{g} \) have the same atomic number 9. Hence, these are isotopes of element X.

Key Concepts

Atomic Number

The atomic number of an element is a fundamental property that defines the identity of the element. It represents the number of protons in the nucleus of an atom. For example, when we look at an element like Fluorine, which is represented as \(_{9}\mathrm{F}\), the number 9 indicates that there are 9 protons in its nucleus.

The atomic number is consistent for all atoms of the same element. Be mindful that it's written as a subscript before the element symbol.

• It is crucial because it determines the chemical properties of the element.
• Every atom of a specific element will have the same atomic number.
• The periodic table is arranged based on atomic numbers, making it a key component in understanding chemical behavior.

Understanding atomic numbers helps in identifying elements and predicting their chemical reactions.

Neutrons

Neutrons are subatomic particles found in the nucleus of an atom, alongside protons. Unlike protons, neutrons have no electrical charge; they are neutral.

Neutrons play a crucial role in the stability of the nucleus. Without neutrons, protons, which repel each other due to their positive charge, couldn't stay bunched together.

• The number of neutrons in an atom can vary, even within the same element. This variation leads to the formation of isotopes.
• To find the number of neutrons in an atom, you subtract the atomic number from the mass number: \( ext{Number of Neutrons} = ext{Mass Number} - ext{Atomic Number} \).
• For instance, fluorine-19 \(_{9}^{19}\mathrm{F}\) has 19 - 9 = 10 neutrons.

Understanding neutrons is essential for comprehending why isotopes exist and how they differ from each other.

Mass Number

The mass number of an atom is the total number of protons and neutrons in its nucleus. It is always a whole number and provides us with an idea of the atomic mass. In chemical notation, the mass number is written as a superscript:

• This number reflects how massive an atom is.
• For example, in the symbol \(_{9}^{19}\mathrm{X}\), 19 is the mass number, indicating that the sum of protons and neutrons is 19.

Mass number helps distinguish isotopes from one another since isotopes have the same atomic number but different mass numbers.

It is important to note that while the atomic number remains constant across all isotopes of an element, the mass number varies because of the difference in the number of neutrons. Understanding the mass number provides insight into how isotopes are identified and how much each isotope of an element weighs.