Problem 24 - Chemistry The Molecular Science

Question

Give the complete symbol \({ }_{Z}^{A} \mathrm{X}\) for each of these atoms: (a) sodium with 12 neutrons, (b) argon with 21 neutrons, and (c) gallium with 38 neutrons.

Step-by-Step Solution

Answer

Sodium: \\( { }_{11}^{23} \mathrm{Na} \\); Argon: \\( { }_{18}^{39} \mathrm{Ar} \\); Gallium: \\( { }_{31}^{69} \mathrm{Ga} \\).

Step 1: Understand the Atomic Symbol Notation

The symbol \({ }_{Z}^{A} \mathrm{X}\) represents an element, where \({}\^AX\) is the element symbol, \({}^A\) the mass number (the total number of protons and neutrons), and \({}_Z\) the atomic number (the number of protons). To find the complete atomic symbol, we need to determine these values for each element.

Step 2: Calculate for Sodium

For sodium (Na), the atomic number \(Z\) is 11 (since sodium has 11 protons). Given that sodium has 12 neutrons, the mass number \(A\) is the sum of protons and neutrons: \(A = 11 + 12 = 23\). Thus, the symbol is \({ }_{11}^{23} \mathrm{Na}\).

Step 3: Calculate for Argon

For argon (Ar), the atomic number \(Z\) is 18 (since argon has 18 protons). Given that argon has 21 neutrons, the mass number \(A\) is the sum of protons and neutrons: \(A = 18 + 21 = 39\). Thus, the symbol is \({ }_{18}^{39} \mathrm{Ar}\).

Step 4: Calculate for Gallium

For gallium (Ga), the atomic number \(Z\) is 31 (since gallium has 31 protons). Given that gallium has 38 neutrons, the mass number \(A\) is the sum of protons and neutrons: \(A = 31 + 38 = 69\). Thus, the symbol is \({ }_{31}^{69} \mathrm{Ga}\).

Key Concepts

Atomic Number

The atomic number is a fundamental property of an element which defines it uniquely. It is represented by the symbol \( Z \) and signifies the number of protons present in the nucleus of an atom. The atomic number determines the identity of an element. For example, hydrogen always has an atomic number of 1, indicating it has one proton. Similarly, the atomic number of sodium is 11, meaning it has 11 protons.

• The atomic number is crucial because it not only defines the element but also determines its position in the periodic table.
• The number of protons is equal to the number of electrons in a neutral atom, maintaining its electrical neutrality.
• For elements like argon and gallium, their atomic numbers are 18 and 31, respectively, showing their intrinsic properties.

Understanding the atomic number is essential as it provides a foundation for learning about atomic structure and chemical reactions.

Mass Number

The mass number, denoted by \( A \), is the total count of protons and neutrons in an atom's nucleus. It is different from the atomic number, which only counts protons. The mass number helps in determining the isotopic composition of an element. Isotopes are variants of a particular chemical element that have different neutron numbers, and hence different mass numbers, but the same number of protons.

• For instance, with sodium: having 11 protons and 12 neutrons, the mass number is 23.
• The mass number is not found on the periodic table because it is specific to each isotope. For argon, an atom could have a mass number like 39 if it has 18 protons and 21 neutrons.
• In elements like gallium, with a mass number of 69 (31 protons and 38 neutrons), the number reflects its specific atomic mass.

Overall, the mass number is an important concept, especially when discussing isotopes and nuclear chemistry.

Protons and Neutrons

An atom's nucleus contains protons and neutrons, which collectively make up most of the atom's mass. Protons are positively charged particles, while neutrons are neutral, having no charge. Understanding these two fundamental particles is essential for studying the atomic structures of elements.

• Protons determine the atomic number, which identifies the element, for example, sodium with 11 protons.
• Neutrons, on the other hand, contribute to the mass number. Sodium has 12 neutrons, combining with its protons to form a mass number of 23.
• Neutrons can vary even within the same type of atom, leading to different isotopes which have important implications in fields like nuclear energy and medicine.
• In argon atoms, where the mass number is 39, neutrons make up a significant portion alongside the element's 18 protons.
• Similarly, gallium has a remarkable number of neutrons, 38, contributing to its overall mass number of 69.

The interaction and quantity of protons and neutrons define many properties of atoms, influencing stability, isotopic abundance, and physical characteristics.