Problem 60 - Chemistry Matter and Change

Question

How is the mass number related to the number of protons and neutrons an atom has?

Step-by-Step Solution

Answer

The mass number is the sum of an atom's protons and neutrons: \( A = Z + N \).

Step 1: Understanding Mass Number

The mass number of an atom is defined as the total number of protons and neutrons present in the nucleus of an atom. It is represented by the symbol \( A \). Each proton and neutron contributes approximately one atomic mass unit (amu) to the mass number.

Step 2: Identifying Components

To find the mass number, one needs to identify the number of protons, which is equal to the atomic number (represented by \( Z \)) of the element, and the number of neutrons, which can vary in isotopes of the same element.

Step 3: Relation Formula

The relationship between the mass number \( A \), the number of protons \( Z \), and the number of neutrons \( N \) is given by the formula: \[ A = Z + N \] This equation shows that mass number is the sum of the protons and neutrons.

Step 4: Example Calculation

Consider an isotope of carbon: Carbon-14. Here, the atomic number \( Z \) for carbon is 6 (which means it has 6 protons). The mass number \( A \) for Carbon-14 is 14. Using the formula \( N = A - Z \), we can find the number of neutrons: \[ N = 14 - 6 = 8 \] So, Carbon-14 has 8 neutrons.

Key Concepts

Protons

Protons are one of the key building blocks of an atom. They are located in the nucleus, the dense center of an atom. Each proton carries a positive electric charge, which is symbolized by the symbol \(+\). This positive charge plays a crucial role in defining the chemical behavior of an atom.

The number of protons in the nucleus is referred to as the atomic number, denoted by \( Z \). This number is unique for each element on the periodic table and determines the identity of the element. For example:

• Hydrogen, the simplest element, has 1 proton.
• Helium has 2 protons.
• Carbon has 6 protons.

Hence, if an atom has 6 protons, it is unmistakably carbon. Understanding protons are essential for grasping how elements differ and why they behave in certain ways chemically.

Neutrons

Neutrons are subatomic particles, similar in size to protons, that reside in the atomic nucleus. Unlike protons, neutrons have no electrical charge – they are neutral. This lack of charge means neutrons do not influence the atomic charge or chemical properties directly.

The number of neutrons in an atom can vary even among atoms of the same element, leading to different isotopes. These variations do not affect the element’s identity but can affect its mass. For instance:

• Carbon-12 has 6 neutrons.
• Carbon-14 has 8 neutrons.

You can calculate the number of neutrons in an atom using the formula: \[ N = A - Z \] where \( A \) is the mass number and \( Z \) is the atomic number. Neutrons add to the atomic mass but not the electric charge.

Atomic Number

The atomic number, represented by the symbol \( Z \), is fundamental to identifying an element. It tells us how many protons are in the nucleus of an atom. The atomic number is never the same for two different elements. This distinct number ensures that each element has a unique position on the periodic table.

Besides identifying elements, the atomic number also helps in predicting an element's chemical properties and its place in the periodic table. For example:

• Gold, with an atomic number of 79, always has 79 protons regardless of its isotopic form.
• Any atom with 1 proton is hydrogen with an atomic number of 1.

Understanding the atomic number helps you navigate the periodic table and explore the properties of elements and their reactions accurately.

Isotopes

Isotopes are variants of a particular chemical element that differ in neutron number, although they share the same number of protons. This means isotopes have the same atomic number but different mass numbers due to the difference in neutrons.

Isotopes occur naturally and can exhibit different properties, especially in terms of stability and radioactive behavior. For instance, some isotopes might be stable while others are radioactive. Examples include:

• Carbon-12, which is stable, and Carbon-14, which is radioactive.
• Uranium-235 and Uranium-238, differing in stability and applications like nuclear energy.

Isotopes are significant in scientific applications, from dating ancient artifacts using Carbon-14 to medical diagnostics using various radioactive isotopes. Grasping what isotopes are enables deeper insight into both the stability and instability of elements.