Question

State the number of neutrons in an atom of each of the following isotopes: (a) \(\quad{ }_{11}^{23} \mathrm{Na}\) (b) \(\quad{ }_{30}^{65} \mathrm{Zn}\) (c) \(\frac{27}{13} \mathrm{Al}\) (d) \({ }_{47}^{107} \mathrm{Ag}\)

Short answer

(a) 12 neutrons, (b) 35 neutrons, (c) 14 neutrons, (d) 60 neutrons.

Step-by-step solution

Understanding Isotopic Notation

Isotopic notation is represented as \( _{Z}^{A}X \), where \( A \) is the mass number, \( Z \) is the atomic number, and \( X \) is the chemical symbol. The atomic number \( Z \) represents the number of protons in an atom, and the mass number \( A \) is the total number of protons and neutrons.

Determine Number of Neutrons in Sodium

For \( _{11}^{23} ext{Na} \), the atomic number \( Z = 11 \) and the mass number \( A = 23 \). The number of neutrons is calculated as \( A - Z = 23 - 11 = 12 \). Thus, the sodium isotope has 12 neutrons.

Calculate Neutrons in Zinc Isotope

For \( _{30}^{65} ext{Zn} \), the atomic number \( Z = 30 \) and the mass number \( A = 65 \). The number of neutrons is \( A - Z = 65 - 30 = 35 \). Therefore, the zinc isotope has 35 neutrons.

Compute Neutrons in Aluminum Isotope

Analyzing the isotope \( _{13}^{27} ext{Al} \), we identify \( Z = 13 \) and \( A = 27 \). Therefore, the number of neutrons is \( A - Z = 27 - 13 = 14 \). The aluminum isotope has 14 neutrons.

Evaluate Neutrons in Silver Isotope

For \( _{47}^{107} ext{Ag} \), where \( Z = 47 \) and \( A = 107 \), the number of neutrons can be found with \( A - Z = 107 - 47 = 60 \). Therefore, the silver isotope has 60 neutrons.

Key concepts

Neutrons Calculation

Understanding how to calculate the number of neutrons in an atom requires a grasp of the isotopic notation. Each isotope is denoted by the formula \( _{Z}^{A}X \), where \( A \) is the mass number and \( Z \) is the atomic number. The mass number, \( A \), equals the sum of the protons and neutrons in the nucleus. Utilizing this notation, the number of neutrons can be determined by subtracting the atomic number from the mass number: \( ext{Number of Neutrons} = A - Z \).
For example, in the sodium isotope \( _{11}^{23} \mathrm{Na} \), the atomic number \( Z = 11 \) (indicating 11 protons), and the mass number \( A = 23 \). The neutrons calculation is \( 23 - 11 = 12 \) neutrons.
Similarly, for the zinc isotope \( _{30}^{65} \mathrm{Zn} \), the process involves \( A = 65 \) and \( Z = 30 \), leading to \( 65 - 30 = 35 \) neutrons. By using this simple subtraction method, you can determine the neutron count of any isotope. It's a straightforward approach grounded in basic properties of atomic structure.

Atomic Structure

The structure of an atom is central to understanding its properties and behavior. The atomic structure can be divided into three main components: protons, neutrons, and electrons.

• Protons are positively charged particles found in the nucleus. The number of protons defines the atomic number \( Z \) and therefore the element itself.
• Neutrons are neutral particles, also located in the nucleus, contributing to the mass of an atom but not affecting its electrical charge.
• Electrons are negatively charged particles that orbit the nucleus in energy levels or shells. Their arrangement determines the atom's reactivity and bonding properties.

Understanding these components is fundamental in exploring how atoms interact. The nucleus, composed of protons and neutrons, forms the dense center of an atom, while electrons, which are much lighter, travel around the nucleus creating an electron cloud. This structural arrangement highlights why the mass of an atom is primarily concentrated in its nucleus.

Mass Number

The mass number is a vital concept when discussing different isotopes of an element. Represented by \( A \), the mass number is the sum total of an atom's protons and neutrons.
For instance, in isotopic notation \( _{Z}^{A}X \), \( A \) specifies the mass number, providing information about the isotope's total atomic mass. It is crucial to understand that while the atomic number \( Z \) remains constant for a given element, denoting the element's identity and proton count, the mass number can vary among isotopes.
An alteration in the number of neutrons leads to different isotopes of the same element, each with a unique mass number. Take carbon as an example, where Carbon-12 and Carbon-14 are isotopes with mass numbers 12 and 14, respectively, due to differing neutron counts. The concept of the mass number is essential in identifying and distinguishing isotopes and plays a significant role in nuclear chemistry and physics.